125 papers
This paper disproves the Perälä–Virtanen conjecture by constructing explicit radial symbols on Bergman and Fock spaces where a positive limit inferior of the Berezin transform fails to guarantee essential positivity, demonstrating that the Berezin liminf criterion is insufficient for radial Toeplitz operators in all complex dimensions.
This paper proves that every bounded continuous tight frame on an infinite-dimensional separable Hilbert space over a metric measure space with specific regularity conditions can be sampled to form a uniformly discrete, nearly tight frame, with applications demonstrating that Gabor systems, wavelet systems, exponential frames, and spectral subspaces of elliptic differential operators all admit such uniform discretizations.
This paper establishes a unified framework for analyzing the commutativity and semi-commutativity of generalized Cauchy singular integral operators on , yielding complete characterizations of quasinormality and product structures for asymmetric dual truncated Toeplitz operators while providing new proofs and improvements for classical results like the Brown-Halmos theorems.
This paper investigates the construction of positive definite thresholding functions for correlation matrices, establishing that preserving positive semidefiniteness through soft-thresholding inevitably induces a geometric collapse in the feature space, thereby limiting the recoverable signal.
This paper formulates a bilinear local smoothing conjecture for Fourier integral operators in all dimensions , demonstrates that the linear conjecture implies this bilinear version, and establishes the conjecture for dimension and all odd dimensions .
This paper establishes the Mosco-convergence of Cheeger energies on Gromov-Hausdorff converging spaces satisfying curvature-dimension conditions by employing a Lagrangian approach that combines Wasserstein geodesic stability with nonsmooth calculus duality, thereby ensuring the continuity of Neumann eigenvalues even in infinite-dimensional settings.
This paper introduces an intrinsic deformation of smooth function algebras on compact Riemannian manifolds via spectral channel twisting, establishes conditions for its extension to Sobolev algebras and associativity, and demonstrates that classical strict deformations arising from abelian group actions are unified as specific instances of this framework.
This paper establishes a sharper upper bound for the amenability constant of the Fourier algebra of discrete groups and uses it to calculate explicit values for new classes of discrete and compact groups, thereby providing further evidence for the conjecture that Runde's lower bound is an equality.
This paper introduces new techniques to provide a unified framework for computing the metric entropy of ellipsoids in Banach spaces, delivering precise asymptotic expansions with explicit constants, improved second-order terms, and the first exact characterization for infinite-dimensional bodies, with significant applications to function classes in Sobolev and Besov spaces and machine learning.
This paper introduces the -transformation, a new integral operator constructed via kernel fusion of the fractional Fourier transform, and establishes its fundamental properties alongside a comprehensive survey of its associated uncertainty principles, including Heisenberg's, Hardy's, Pitt's, and Beurling-Hörmander's theorems.
This paper investigates the local-triviality dimensions of actions on -algebras within noncommutative Borsuk-Ulam theory, demonstrating that free actions do not necessarily possess finite weak local-triviality dimensions and that these invariants can exhibit discontinuity or exceed fiber values in continuous fields, while establishing conditions for upper semicontinuity through examples involving noncommutative tori and spheres.
This short note resolves a problem posed by Wickstead regarding the sequential monotone closure of spaces, a topic arising from the study of Riesz completions of regular operator spaces between Banach lattices.
This paper establishes the existence of nontrivial nonnegative weak solutions to a semilinear Grushin-Schrödinger equation in with controlled potentials by proving the embedding of the associated energy space into a weighted Lebesgue space and deriving subsequent regularity results.
This paper establishes a general Jensen-type inequality for pairs of measure spaces on product domains that extends classical results like Hölder's and Minkowski's inequalities, provides sharp equality conditions and quantitative refinements, and demonstrates applications ranging from entropy-type bounds to convolution operators.
This paper proposes a framework for Haar-type measures on topological quasigroups by introducing quasi-invariant measures with modular cocycles, demonstrating how Moufang-type identities constrain these cocycles to suggest that Kunen's theorem reflects the collapse of modular defects into a loop structure.
This paper establishes sufficient and, in some cases, necessary conditions for the continuity and compactness of embeddings between various scales of generalised Morrey smoothness spaces on bounded smooth domains, utilizing wavelet characterisations to generalise and improve upon existing results for classical smoothness Morrey spaces.
This paper establishes the discrete Rubio de Francia extrapolation theorem for pairs of quasi non-increasing sequences with weights and provides a weight characterization for the boundedness of the generalized discrete Hardy averaging operator on such sequences within the space .
This paper investigates a linear operator derived from invariant measures under multidimensional transformations, using its iterates to provide an explicit solution for the associated functional equation and to establish the existence of absolutely continuous invariant measures that generalize classical -adic maps to higher dimensions.
This paper investigates generalized b-weakly compact operators on locally convex-solid Riesz spaces by providing new characterizations and introducing KR-spaces to establish a factorization theory analogous to that of b-weakly compact operators through KB-spaces.
This paper constructs a family of parametric extensions of coboundary operators for double complexes of meromorphic functions on higher genus Riemann surfaces by utilizing Schottky uniformization and the algebraic completion of an infinite-dimensional Lie algebra module.