125 papers
This paper demonstrates that entropy acts as a driving force in various evolution equations because it characterizes the invariant measure of an underlying stochastic process, thereby unifying diverse examples from stochastic processes, gradient flows, and GENERIC systems under a single principle.
This paper investigates the subnormality of quotients of -invariant Hilbert modules by homogeneous polynomials, establishing that such quotients are subnormal only if the polynomial is square-free and of degree at most one for standard spaces like the Hardy and Drury-Arveson modules, while also demonstrating that higher-degree examples exist for specific invariant modules like the Dirichlet module.
This paper proves the author's conjecture that every compact primitive of a Stepanov remotely almost periodic function with a minimal -limit set is itself remotely almost periodic, thereby resolving the problem of integrating such functions.
This paper addresses open questions regarding strict spectral approximants by computing the subdifferential of the Ky Fan - norm to establish characterizations for best approximations and derive necessary and sufficient conditions for -orthogonality.
This paper confirms the nearly 30-year-old 100 Euro Conjecture by proving that for every real matrix satisfying , there exists a nonzero vector such that entrywise, utilizing a finite-dimensional reformulation of Ball's plank theorem.
This paper establishes sharp uniform bounds on the eigenvalues of time-frequency localization operators and coherent state transform localizations near their spectral phase transition, revealing a qualitative difference in their decay rates where the former exhibits a logarithmic dependence while the latter decays quadratically.
This paper summarizes existing results and open questions regarding isometric embeddings between Schatten classes, provides an overview of relevant methods, and establishes a new non-embeddability result using a novel approach.
This paper demonstrates that the -convexification of Gowers' space yields Banach spaces with unique unconditional bases containing block bases with spreading models distinct from , , and , thereby resolving a long-standing open problem by Bourgain et al. and disproving the conjecture that such spaces must be isomorphic to their squares.
This paper defines and analyzes a class of continuous functions on constructed via an infinite stochastic matrix and specific parameters, establishing criteria for their monotonicity, differentiability, and singularity while investigating the properties of their level sets.
This paper establishes a universal approximation theorem proving that shallow neural networks with inputs in a topological vector space and outputs in a Hausdorff locally convex space are dense in the space of continuous mappings on compact subsets, thereby generalizing existing scalar-valued results to include Banach and Hilbert-valued approximations.
This paper extends the Stockwell transform to the setting of Gelfand pairs, investigates its key properties, and analyzes the associated localization operators within this framework.
This paper investigates linear preserver problems on the space of Toeplitz matrices over real or complex fields, providing characterizations for preservers of rank-one matrices and determinants while also discussing related results for other structured matrices.
This paper establishes that sufficiently large margins enable learnability in arbitrary metric spaces based solely on the triangle inequality, reveals a sharp threshold for learnability in linear combinations of distance functions, and demonstrates that not all margin-based learning can be reduced to linear classification in Banach spaces by proving that learnability in such spaces implies polynomial sample complexity scaling with the inverse margin.
This paper proves that every semi-normalized unconditional Schauder frame in an infinite-dimensional Hilbert space contains a subsequence that forms a frame, and applies this result to resolve open questions regarding the non-existence of such frames for specific Gabor systems, exponential systems, and translation-invariant subspaces under critical density conditions.
This paper investigates the automatic boundedness of operators mapping from ordered vector spaces to topological vector spaces, with a specific focus on order-to-topology bounded and continuous operators, as well as Levi and Lebesgue operators.
This paper investigates matrices and operators satisfying the Kreiss condition with constants arbitrarily close to one, establishing refined lower bounds for power growth and demonstrating that specific variants of the condition guarantee similarity to a contraction when the spectrum touches the unit circle at a single point, utilizing a positivity argument involving the double-layer potential operator.
This paper extends the Gale-Nikaido-Kuhn-Debreu market equilibrium theorem to a broader class of economies by generalizing previous results to commodity spaces modeled by any Hausdorff topological vector space with a nontrivial continuous dual, rather than restricting them to locally convex Hausdorff spaces.
This paper investigates the topological boundedness and the uniform boundedness principle for operators that are order-to-topology bounded or continuous, mapping from ordered vector spaces to topological vector spaces.
This paper introduces a new class of generalized Hilbert matrix operators induced by a positive finite Borel measure on (0,1) acting on weighted sequence spaces and establishes a necessary and sufficient condition for their boundedness, thereby extending recent related results.
This paper establishes that order-to-weak continuous operators from an ordered Banach space to a normed space are automatically bounded under relatively mild conditions.