Papers

We develop a tensor reduced-order modeling (TROM) framework for optimization-based inverse problems governed by parameter-dependent dynamical systems. The approach approximates the parameter-to-observation map directly in tensor-train (TT) format using TT-SVD or TT-Cross and integrates it into a regularized nonlinear least-squares formulation. Beyond accelerating forward evaluations, the low-rank tensor structure reformulates the inverse problem in reduced coordinates, assembles Gauss–Newton quantities without forming the full observation-space Jacobian, and minimizes the TROM objective over the discrete parameter grid. This tensor optimization provides either a stand-alone approximate solution or a data-informed initialization for a subsequent Gauss–Newton solve. We study an inverse heat-transfer problem in a heterogeneous medium, where the parameters describe the locations and radii of low-conductivity inclusions, and a FitzHugh–Nagumo parameter-estimation problem with a highly nonconvex landscape. Numerical experiments assess reduced-order model error, measurement noise, regularization, initialization, spatial discretization, and increasing parameter dimension. The results show that TROM reproduces full-order inversion at substantially reduced online cost. They also demonstrate that reduced-coordinate inversion, tensor-based optimization, and appropriate regularization improve robustness in higher-dimensional, noisy, and strongly nonconvex regimes. For the continuous TROM inverse problem, we develop an error-to-inversion analysis. Under local strong convexity of the regularized FOM objective and parametric smoothness of the FOM observation map, the error between the parameters recovered with the full-order model and TROM is bounded by controlled uniform errors in the surrogate map and its Jacobian, together with local FOM and curvature quantities.

We study the magnetic Neumann Laplacian in an infinite planar sector of opening $\alpha\in(0,\pi)$ under a constant magnetic field. Building on earlier work by Bonnaillie-Noël and collaborators and by Exner, Lotoreichik, and Pérez-Obiol, we prove that the bottom of the spectrum lies strictly below the half-plane threshold for every convex sector. Consequently, $H_\alpha$ has a discrete ground-state eigenvalue for every $0<\alpha<\pi$. This resolves the bound-state problem for convex sectors, a model problem arising in the analysis of magnetic localization near corners and of the third critical field in type-II superconductivity.

We study a pinned form of graceful labeling. For full binary trees, we ask whether some deepest root-to-leaf path can carry the alternating extreme pattern $0,n-1,1,n-2,\dots$. Such a spine uses the extreme labels and largest differences, forcing all off-spine vertices and edges to use the middle labels and smaller differences, respectively. We prove this pinned-spine conjecture for comb full binary trees, verify it computationally for all rooted non-isomorphic full binary trees through order $23$, and give an example showing that a pinned-spine labeling cannot always be chosen as an $\alpha$-labeling. For spider trees, we prove a packing theorem for self-matched legs: pairwise disjoint legs based at hub label $1$, at least one of which contains label $0$, can be combined into a graceful spider, with unused labels attached as hub leaves. This yields graceful labelings for mixed-length spiders with sufficiently many leaves. We also report computations using a depth-first search ordered by largest unused differences and formulate the six-arm problem as an offset five-arm residual problem.

For moving-load problems whose geometry and material properties are approximately invariant along the traveling direction, 2.5D analysis retains three displacement components at lower cost than full three-dimensional discretization. We present a 2.5D Non-Uniform Rational B-spline (NURBS)-trace infinite-element method (NBIEM), formulated as a coupled finite/infinite-element scheme, for wave propagation in linear viscoelastic semi-infinite geotechnical media. The bounded near field is discretized by isogeometric analysis, while the exterior is represented by tensor products of the boundary NURBS basis and admissible outgoing or evanescent exponential radial functions. Both subdomains share the same NURBS trace space and control-point degrees of freedom, enforcing displacement continuity without projection or mortar variables. For the selected radial functions, far-field stiffness and mass contributions are evaluated through closed-form radial moments, eliminating finite radial cutoff and radial quadrature. Closed-form half-space solutions verify displacement and stress frequency-response functions in sub-Rayleigh, super-shear but sub-compressional, and super-compressional moving-load regimes. Low-frequency studies assess sensitivity to radial parameters and artificial-boundary placement. Additional tests examine complex-valued response accuracy, phase fidelity, computational cost, and the frequency-dependent working range of the default S-wave-informed exterior realization. Applications to layered media, track–subgrade systems, and buried structures demonstrate the ability to handle heterogeneous materials, multi-patch configurations, curved interfaces, and cover-depth-dependent geotechnical responses. The framework provides a geometrically consistent and computationally efficient treatment of moving-load wave propagation and soil–structure interaction in semi-infinite domains.

We show that driven qubit junctions enable programmable control of physical entropy transport, with entropy conductance governed by quantum dynamics rather than by reservoir parameters alone. By comparing two simple quantum architectures – a driven single-qubit junction and a driven two-qubit junction – we find that the two-qubit junction enhances entropy transfer while requiring substantially lower driving power than its single-qubit counterpart. We further reveal two non-intuitive effects in both junctions: a sizable coherent contribution to the entropy current that emerges only under resonant driving, and negative differential entropy conductance, where increasing the thermal bias suppresses entropy flow into the probe reservoir. These results identify quantum logic architectures as programmable devices for entropy transport and suggest routes toward quantum feedback control, reservoir protection and refrigeration in driven quantum circuits.

We study the long-time behavior of the Wasserstein gradient flow of the squared Maximum Mean Discrepancy (MMD) between a probability measure $\rho$ and a target measure $\mu$, where the underlying kernel is given by a Coulomb potential. For $L^\infty$ target densities $\mu$, we establish the existence of global weak solutions starting from arbitrary Borel probability measures and prove that the density $\rho_t$ belongs to $L^\infty$ for any $t>0$. We also show that the Hölder norm can grow exponentially in time. On the flat torus ${\mathbb{T}}^\mathsf{d}$, we prove a global metric PL inequality for every finite-Coulomb-energy source and nearly uniform target. For general bounded, uniformly positive targets, we prove exponential decay of the squared MMD without requiring a lower bound on the initial data, using a defective PL inequality. We also prove that the usual PL inequality may fail when the target vanishes only at one point and that, when $\mathsf{d}\ge2$, no PL constant can hold uniformly over all targets satisfying a prescribed lower bound. On ${\mathbb{R}}^\mathsf{d}$, for $\mathsf{d}\ge2$, under radial symmetry, source-support inclusion, and target-positivity assumptions, we establish a PL inequality and exponential convergence. On the unrestricted whole-space class, neither a multiplicative squared-MMD decay modulus uniform over the initial datum nor a global PL inequality can hold. Finally, in every dimension and in both spatial settings, we prove that every Lagrangian critical point coincides with the target when $(\rho-\mu)^+$ is absolutely continuous. In dimension two, the energy supplies uniform tightness. This implies that if our constructed solutions have finite energy at some positive time, then they converge to the target narrowly and strongly in negative-order Sobolev spaces.

This survey revisits classical results on the existence of periodic solutions in incompressible fluid dynamics. Owing to the breadth of the subject, we restrict our attention to the simplest and most illustrative framework: the two-dimensional Euler equations and vortex patch solutions. The aim is not to present new results, but rather to provide a unified and streamlined exposition of several classical constructions by combining ideas from the original works with more recent developments.

The paper studies martensitic microstructures in polycrystals, focussing on their compatibility across grain boundaries. After a reduction to the case of a planar grain boundary, the case when the grain boundary separates two constant gradients of zero energy is considered. It is shown that for cubic-to tetragonal transformations such a configuration can occur when the relative grain rotation is not in the cubic group. Then the case when the grain boundary separates two simple laminates of zero energy is considered, it being shown using a computer-assisted symbolic calculation that in the cubic-to-tetragonal case compatibility is only possible for a closed set of measure zero in the manifold of grain boundary normals and relative grain rotations, and that a similar slightly weaker result holds for cubic-to-orthorhombic transformations. The results suggest why higher-order laminates are often observed for such transformations. The Taylor set of deformation gradients is defined and studied, this set having the property that any deformation whose gradient belongs to it corresponds to a zero-energy microstructure for the polycrystal independent of grain geometry and grain rotations. New upper bounds for the Taylor set are proved for cubic-to-tetragonal and cubic-to-orthorhombic transformations, generalizing those of Bhattacharya and Kohn using the geometrically linearized theory. We give a simple proof of a related result of Peigney characterizing the positive diagonal matrices in the quasiconvex hull of the energy wells for cubic-to-tetragonal transformations.

Multiscale problems are notoriously difficult to tackle using traditional numerical methods, as accurately resolving fine-scale features often requires prohibitively fine discretizations. This challenge is particularly pronounced in applications such as materials science, fluid dynamics, climate systems, chemical processes, and complex networks. Recent neural operator models provide a promising data-driven alternative, but frequently struggle to achieve sufficient accuracy in the presence of strongly heterogeneous or oscillatory coefficients. In this work, we focus on the solution of elliptic PDEs with rough and high-contrast inputs. The Localized Orthogonal Decomposition (LOD) method is a well-established numerical approach for such problems, but it comes, however, at a substantial computational cost. We investigate the performance of popular neural operator architectures on these challenging multiscale problems and identify key limitations in their ability to resolve fine-scale structure. To overcome these challenges, we introduce LOD-MSNO (LOD-Multiscale Neural Operator), a hybrid approach that leverages the LOD method as a strong multiscale prior by building on its representation of the solution as a linear combination of problem-adapted basis functions, while addressing its main computational bottlenecks through data-driven operator learning. We further provide theoretical error estimates for the proposed coefficient-learning framework. Lastly, we demonstrate the potential of our proposed method to outperform current neural operator baselines in terms of accuracy for challenging multiscale inputs, while mainly retaining the computational efficiency of neural operator models.

For a fixed integer $j\ge1$ and $0<p<1$, we study the probability generating function (pgf) equation \[ (1+2p)\,g(x)=2p\,x^{j}+g\bigl(x-px+px^{2}\bigr),\qquad 0\le x\le1 , \] which governs the limiting degree distribution $\{p_k\}$ of a family of evolving network models. The cases $j=1$ and $j=2$ are the treelike fast-growth model of Feng and Hu and the homogeneous evolving network of Feng, Li and Hu. We prove that for every $j$ the equation has a unique pgf solution, of mean $2j$, and we determine its coefficient tail exactly: \[ p_k=k^{-1-\rho}\,\Psi_j(\log_\lambda k)+o\bigl(k^{-1-\rho}\bigr), \] where $\lambda=1+p$, $\rho=\log(1+2p)/\log(1+p)$ is independent of $j$, and $\Psi_j$ is continuous, strictly positive and $1$-periodic, with explicit Fourier coefficients. This resolves two conjectures of Feng and coauthors: (1) the power-law order $p_k=\Theta(k^{-1-\rho})$ and (2) its refinement to the multiplicatively periodic form $p_k\sim\Psi_j(\log_\lambda k)\,k^{-1-\rho}$. The periodic factor is genuinely non-constant for $p$ near $1$, and, for the two network models, for all $p$ outside a discrete set. Consequently, $p_k$ is asymptotic to no constant multiple of $k^{-1-\rho}$. Our method is a self-contained local analysis of the supercritical Galton-Watson process with offspring law $1+\mathrm{Bernoulli}(p)$, inspected at an independent geometric time. This time-changed process solves the equation observed by Feng and coauthors. The main results of this paper were obtained by the multi-agent system Eureka and have subsequently been verified by the authors.

We prove the Gonality Conjecture in arithmetic dynamics: for any non-isotrivial one-parameter algebraic family of rational maps on $\mathbb{P}^1_{\mathbb{C}}$, the gonality of distinct dynatomic curves tends to infinity. More generally, outside the flexible Lattès family, every small sequence of horizontal curves has gonality tending to infinity, and its genus grows superlinearly with its degree over the parameter curve. We also obtain higher-dimensional analogues under natural bifurcation and multiplier-genericity hypotheses. As applications, we prove uniform boundedness results for iterated preimages over number fields and geometric uniform boundedness results for preperiodic points over function fields. The proof combines arithmetic equidistribution, woven currents, and bifurcation theory; the bifurcation mechanism is what forces the growth of genus and gonality.

This paper establishes a rigorous, unified geometric framework for quantum state spaces by constructing smooth, regular embeddings into higher-order dual number algebras $\mathcal{Q}_N \equiv \mathbb{R}[\varepsilon]/(\varepsilon^{N^2-1})$, wherein every quantum state is faithfully represented as a non-reduced scheme-theoretic point. We show that under this unified family of truncated rings, the non-linear matrix commutators governing the Liouville-von Neumann dynamics map globally onto flat, linear, and rigid algebraic flows, establishing nilpotent dual algebras as a pristine geometric landscape for higher-dimensional quantum kinematics. As $N \to \infty$, this family converges to a Cauchy-complete power series ring $\mathcal{Q}_\infty$, where non-Archimedean completion linearizes the phase space, aligning the Fubini-Study geometry with the classical Fisher-Rao manifold.

With the development of artificial intelligence (AI) techniques, neural receivers, which apply AI to improve wireless receivers have been developed. However, most existing neural receivers apply deep learning only to the outer receiver while retaining conventional channel decoding for the inner receiver, which prevents joint optimization and makes it difficult to build efficient and unified AI-native receivers. To address this issue, we propose a foundation model (FM)-enabled unified neural receiver, FM-Receiver, that integrates the outer and inner receivers into a single AI-native framework, by leveraging the strong representation capability of FMs. Specifically, we introduce a grouped error correction code Transformer that performs symbol-level channel decoding, enabling seamless integration of the inner and outer receiver. Building on this, we illustrate the proposed FM-Receiver, that directly takes the received signals as input of FM and outputs the recovered transmitted bits. In addition, a three-stage configuration-adaptive pre-training strategy is designed to improve the generalization ability to diverse system configurations and scenarios. Extensive simulations show that the proposed FM-Receiver achieves better performance than baselines across different system configurations. It also demonstrates strong zero-shot generalization to unseen frequency bands and scenarios.

We study the well-posedness theory of a coupled modulated Korteweg-de Vries (KdV) system on the circle with a time non-homogeneous modulation acting on the linear dispersion term. When the coupling parameter is equal to one, it has been recently proved that given any $s\in \mathbb{R}$, the resulting modulated KdV system is globally well-posed in $H^s(\mathbb{T})\times H^s(\mathbb{T})$, with a sufficiently irregular modulation. For couplings different from one, we use Diophantine conditions to characterize the resonances and prove that (under further restrictions on the coupling constant) for any $s\in \mathbb{R}$ the coupled modulated KdV system is globally well-posed in $H^s(\mathbb{T})\times H^s(\mathbb{T})$. This result differs from its unmodulated counterpart where it is known that global well-posedness holds for $s\ge s_*\in (5/7,1]$.

In this paper, we study dual semismooth Newton (SSN) methods for degenerate polyhedral projection problems, where generalized Jacobians of the dual residual may remain singular even arbitrarily close to the solution set. Rather than regularizing these singular systems, we exploit the nonuniqueness of the dual representation. We introduce a primal–dual lifted projection-equivalent set that always possesses extreme points without additional structural assumptions on the polyhedron, and show that its extreme-point geometry identifies dual representatives at which nonsingular generalized Jacobians of the dual residual can be constructed. This geometry is further linked to a full-column-rank condition and a generalized weak strict Robinson constraint qualification, showing that the regularity required by the Newton step can be recovered rather than imposed a priori. We also establish displacement bounds that connect representative selection throughout the algorithm with the local Newton mechanism. Building on this variational framework, we develop an inexact dual SSN method with local superlinear convergence and a globalized version combining monotone representative selection with a Wolfe line search. The resulting method is globally convergent and eventually recovers the fast local rate. Numerical experiments on regularized optimal transport, battery-scheduling feasibility restoration, and occupation-measure projection demonstrate its robustness in highly degenerate settings.

The key-value (KV) cache is the dominant memory bottleneck in long-context language model inference. Existing compression methods apply low-rank factorization or quantization independently, without jointly allocating rank and precision under a shared storage budget. We introduce JoLT, a training-free compressor that treats grouped prefill caches as fourth-order tensors and applies partial Tucker decomposition along the token and feature modes, the two axes that carry low-rank structure, while leaving the head and layer modes intact. A rotated low-bit quantizer captures the truncation residual, and a single Lagrangian dual allocates per-group Tucker ranks and residual bit-widths under a global byte constraint. FlashJoLT replaces the exact token-mode SVD with a randomized approximation that matches JoLT within the free zone at a fraction of the compression cost, and a fused Triton decode kernel evaluates attention directly over the stored factors without materializing dense KV tensors. Across five models from four architecture families, covering multi-head attention, grouped-query attention, and mixture-of-experts architecture, JoLT achieves 2 - 3x compression with less than 0.2% perplexity degradation, without retraining. On RULER at 64K context with LLaMA-3.1-8B, retrieval accuracy remains near-lossless through 3x and declines by only 0.90 and 2.40pp at 4x and 5x, respectively. JoLT demonstrates that tensor-aware low-rank decomposition and quantized residuals, unified under a single storage budget, achieve near-lossless KV-cache compression across diverse model architectures without retraining.

We investigate the capacity of an integrated sensing and communication system operating with orthogonal frequency division multiplexing, where the integrated sidelobe level of the transmit signal is adopted as an input cost. The problem is reduced to the capacity of a complex additive white Gaussian noise channel under power and kurtosis constraints. The sensing-optimal and communication-optimal operating points are characterized by circularly symmetric constant-modulus and complex Gaussian inputs, respectively, while the capacity-achieving input in between has discrete amplitude support with a concentric multi-ring geometry. We propose the superposition of the two extremal inputs as a simple and tunable signaling strategy, whose rate admits an exact expression via successive decoding. Numerical results show that the proposed strategy attains a worst-case gap of approximately 0.043 bits to the capacity.

We prove local second-order regularity near the critical set for widely degenerate elliptic systems, and show that this degenerate region has zero Lebesgue measure provided the source term is non-vanishing.

We propose a residual energy-based framework for constructing low-rank approximations of kernel matrices arising from continuous kernel functions. The method operates in a continuous setting and is based on the adaptive selection of pivot nodes, referred to as optimal nodes, which are chosen to minimize the residual energy at each step. This leads to a sequence of rank-$1$ updates of the residual kernel and admits a natural interpretation as a continuous analog of Adaptive Cross Approximation (ACA). From a theoretical perspective, we show that the residual kernels remain in the class of compact operators and that the approximation error is exactly characterized by the residual energy. We provide convergence guarantees showing that the method yields monotonic error reduction under an alignment condition and achieves geometric decay under practically motivated assumptions. Extensive numerical experiments demonstrate that the proposed method achieves approximation errors close to those of the truncated singular value decomposition across a range of kernel functions. The method exhibits strong robustness with respect to sampling and maintains stable performance across different discretizations. Furthermore, the close agreement between the continuous residual energy and the discrete approximation error highlights the consistency of the formulation. These results establish the proposed approach as a theoretically grounded, practically effective continuous counterpart to classical cross-approximation techniques.

In this paper, we prove a sufficient condition for the uniform ball-covering property of closed operator subspaces invariant under selected truncations. We use uniform convexity of the range space and near-contractive finite-rank projection approximations to obtain quantitative coverings with finite-rank centres whenever the truncated images are separable. A weak-star version gives the same covering parameters for quotients by arbitrary weak-star closed subspaces. In the completely bounded setting, the covering parameters are independent of the matrix level. In particular, the duals of all closed subspaces of $S_1(\ell_2)$ admit coverings with centre norm $2$ and radius $1+\varepsilon$, for $0<\varepsilon<1$, at every matrix level. Applications include operator-valued Schur multipliers and, for $1<p<\infty$, prescribed-support Fourier multipliers on countable amenable groups and finitely generated free groups. The Fourier coverings have finite-support centres in the given operator or completely bounded norms. An endpoint example shows failure of the ball-covering property at $p=1,\infty$.

In this article, several upper bounds for the Berezin numbers of bounded linear operators on reproducing kernel Hilbert spaces are obtained through the use of interpolation paths of symmetric means and Orlicz functions. With suitable selections of these paths and functions, we show that the results presented here refine and generalize several earlier known findings. Furthermore, we derive some Berezin number inequalities for such operators using refined Young's inequalities.

We introduce a Tricomi-type generalized fractional calculus in the Sonine kernel framework. The key result is that the Tricomi branch is a Stieltjes function in the admissible parameter range, so its reciprocal is a complete Bernstein function. This fact induces a Sonine fractional calculus together with the canonical Tricomi integral and the associated Riemann–Liouville-type and Caputo-type derivatives. We also prove that, within the Kummer class, the Tricomi branch is the unique Stieltjes representative, once the natural asymptotic normalization is fixed, and we derive the corresponding Lévy–Khintchine representation, Volterra formulation, and scalar Cauchy problem. A distinctive feature of the resulting operators is the emergence of two independent asymptotic orders.

The Batyrev–Kontsevich theorem asserts that birational Calabi–Yau varieties have the same Hodge numbers. In this article, we prove an analogue for Landau–Ginzburg models $(U,f)$, where $U$ is a smooth quasi-projective complex variety and $f$ is a regular function on $U$. Under a natural non-degeneracy assumption, we show that the classes of such models in the localized Grothendieck ring of complex algebraic varieties with exponentials are invariant under crepant birational equivalences. Consequently, the irregular Hodge numbers of the twisted de Rham cohomology $\mathrm{H}^k_{\mathrm{dR}}(U,f)$ are invariant as well.

We provide sharp bounds on the dimension of the abnormal set for rank $2$ polarizations on metabelian Lie groups, establishing the Sard property for the end-point map of such groups. The proof is based on a novel approach that makes essential use of tools from tame geometry. We also obtain bounds for the dimension of the Goh-abnormal set for metabelian Lie groups where the codimension of the derived subgroup is at most $2$, with no assumption on the rank of the polarization. We thus infer that these polarized groups, equipped with sub-Riemannian structures, satisfy the minimizing Sard property.

We investigate valued-field structures on Urysohn universal ultrametric spaces. We introduce $p$-adic Levi–Civita fields as subfields of $p$-adic Hahn fields and treat them together with ordinary Levi–Civita fields. For a subgroup $G$ of $\mathbb{R}$ containing $\mathbb{Z}$ and a countably infinite perfect field $k$, the corresponding Levi–Civita valued field is isometric to the $R$-Urysohn universal ultrametric space, where $R=\{0\}\cup\{\eta^{-g}\mid g\in G\}$. Thus these spaces admit field structures extending prescribed prime valued fields, including $\mathbb{Q}$ with the trivial valuation and the $p$-adic fields $\mathbb{Q}_{p}$. We also prove that complete valued fields with infinite residue fields are haloed, and hence universal for separable ultrametric spaces with corresponding distance sets. In the separable case, such a valued field is itself isometric to the corresponding Urysohn space. Examples include $\mathbb{C}_{p}$, the completion of the maximal unramified extension of $\mathbb{Q}_{p}$, Laurent series fields, and completions of their algebraic closures. Finally, for a countably infinite perfect residue field, the corresponding full Hahn-type valued field is a Urysohn universal ultrametric space exactly when its value group is order-isomorphic to $\mathbb{Z}$.

In this paper, we compute the Möbius function on the poset of pseudo-Levi subgroups containing a fixed maximal torus of two families of finite groups, $GL_n(q)$ and $Sp_{2n}(q)$, for some natural number $n$ and a prime power $q$, where $q>2n+1$. For the general linear group, we consider arbitrary tori, but for symplectic groups, we restrict to tori corresponding to the bipartitions of $n$ into odd integers. Also, we assume $q$ is even for the case of symplectic groups. The Möbius function for the set of pseudo-Levi subgroups of a finite group $G$ is important for an explicit evaluation of the formula expressing the decomposition of tensor products of characters, as proved in Theorem 2 of the paper ”Multiplicity of characters of finite reductive groups and Drinfeld doubles” [arXiv:2512.01432].

Let $\mathscr{L}$ be the class of Lindelöf spaces such that $\mathscr{L}$ is closed under finite products. In this paper, we prove that if $G \in \mathscr{L}$ is a strongly topological gyrogroup, then $G$ is range-metrizable. Furthermore, we prove that if $H$ is a strong subgyrogroup of a strongly topological gyrogroup $G \in \mathscr{L}$, then every compact $G_\delta$-set in the quotient space $G/H$ is Dugundji. Finally, for any strongly topological gyrogroup $G$ and any closed strong subgyrogroup $N$ of $G$, if $G \in \mathscr{L}$ and the quotient space $G/N$ is locally compact, then the inequality $w(G/N) \leq c$ is equivalent to the separability of $G/N$. Our results extend the classical results from topological groups to the class of strongly topological gyrogroups in the literature.

We consider a generalization of the notion of submetry tailored to the setting of spacetimes. We show that, under suitable completeness assumptions, Lorentzian submetries between smooth spacetimes correspond to locally C^{1,1} Semi-Riemannian submersions. Moreover, we establish some applications regarding timelike curvature bounds, isometric group actions, acausal foliations and Lorentz-Wasserstein geometry.

In this paper, we investigate the second Hankel determinant, Toeplitz determinants, Hermitian–Toeplitz determinants and the generalized Zalcman functional for a class of normalized biholomorphic mappings on complex Banach spaces. Motivated by recent results for the corresponding class of analytic functions in the unit disk, we establish Banach space analogues of these determinant estimates. Our results extend the one-variable inequalities of Allu, Lecko and Thomas \cite{ALT2022} to the setting of complex Banach spaces, thereby providing higher-dimensional counterparts for the class corresponding to $\mathcal{F}_{O}(\lambda)$.

This paper is devoted to the study of the second Hankel determinant for normalized $\beta$-spirallike mappings on the unit ball of a complex Banach space. Using the relationship between Banach-space holomorphic mappings and corresponding one-variable $\beta$-spirallike functions, we first establish sharp estimates for the initial homogeneous expansion coefficients. These coefficient inequalities are subsequently applied to derive a sharp bound for the second Hankel determinant.