125 papers
This paper establishes a cohomology theory for multipoint connections on complex curves by assuming recursion relations for complex functions, explicitly expressing the results in examples as higher-genus generalizations of elliptic functions derived from functional equations.
This paper investigates the extension of Lipschitz quasiconvex functions from closed convex sets with nonempty interior in finite-dimensional normed spaces, demonstrating that while Lipschitz extensions generally fail unlike in the convex case, the existence of uniformly continuous or continuous extensions is determined by specific geometric properties of the domain set.
This paper establishes a necessary condition for -invariant kernels on Cartan domains to possess the complete Nevanlinna-Pick property by generalizing Kaluza's Lemma and characterizing such kernels through the existence of characteristic functions associated with -contractions.
This paper establishes the conditions for the existence of the asymptotic mean value of ternary digits and identifies an infinite, everywhere dense set of numbers that possess this mean despite lacking a well-defined frequency for their digits.
This paper investigates transformations on the interval and functions that preserve the asymptotic mean of digits in the ternary (or -adic) representation of numbers, establishing the necessary and sufficient conditions for such transformations to belong to this class.
This paper establishes a dimension-independent lower bound on the cotype constant for normed spaces generated by random polytopes with Gaussian vertices, demonstrating that under specific density conditions on the number of vertices relative to dimension, these spaces satisfy a cotype inequality with high probability.
This paper disproves the 2007 conjecture by Huang and Tam that the Frobenius norm of the self-commutator is contractive under the -Aluthge transform by providing a counterexample and establishing quantitative bounds on the ratio of the transformed to the original self-commutator norms.
This paper investigates the structure and properties of a new rearrangement-invariant quasi-Banach space that generalizes Arias-de-Reyna's classical space and explores its relationship with other rearrangement-invariant Banach spaces.
This paper characterizes fractional Malliavin-Watanabe-Sobolev spaces for all by establishing a criterion based on the integrability and fractional differentiability properties of the -transform's Bargmann-Segal norm, thereby bridging Malliavin calculus with white noise analysis and providing practical tools for analyzing objects like Donsker's delta and self-intersection local times.
This paper investigates the topological, metric, and fractal properties of the set of real numbers whose 4-adic digits possess existing frequencies and a specific asymptotic mean, providing an algorithm for constructing such points and establishing conditions for their Lebesgue measure and Hausdorff dimension.
This paper investigates the topological, metric, and fractal properties of subsets of the interval defined by specific asymptotic means of digits in their ternary representations, while exploring their relationship to numbers characterized by fixed digit frequencies.
This paper establishes the Hölder regularity of harmonic functions on both bounded and unbounded post-critically finite (p.c.f.) self-similar sets by proving a generalized reverse Hölder inequality on their induced cable systems, utilizing a method that avoids heat kernel and resistance estimates.
This paper establishes weak and strong elliptic Harnack inequalities for mixed local and nonlocal -energy forms on metric measure spaces by employing the De Giorgi--Nash--Moser method under axiomatic assumptions including the Poincaré and cutoff Sobolev inequalities.
This paper establishes the well-posedness and -based Sobolev regularity for vector-valued fluid dynamics PDEs, including Stokes and Navier–Stokes equations, on closed manifolds of minimal regularity by developing a parametrization-free variational approach that decouples velocity and pressure variables.
This paper characterizes the spectral properties and invariant subspace structure of compressed shifts on nearly -invariant subspaces by employing unitary equivalence, the Frostman shift, the Crofoot transform, and Sz.-Nagy--Foias theory to bridge the gap between classical model space theory and broader function-theoretic settings.
This paper formulates p-adic analogues of three fundamental results in functional analysis and geometry: the Grothendieck Inequality, the Johnson-Lindenstrauss Flattening Lemma, and the Bourgain-Tzafriri Restricted Invertibility Theorem.
This paper establishes Runge-type approximation results for solutions to linear partial differential equations with constant coefficients on spaces of smooth Whitney jets, providing geometric characterizations of density conditions for elliptic, parabolic, and wave operators, and applying these findings to the approximation of holomorphic functions on specific planar domains.
This paper investigates infinite -indexed complexes of spaces equipped with multilinear products to derive hierarchies of differential identities and closed multiple products, ultimately demonstrating how maximal differential orders, powers, and coherence conditions generate families of multi-graded differential algebras.
This paper demonstrates that while internal-external magnetic field separation is unique and stable on a full sphere, it becomes non-unique without prior assumptions and highly unstable even with reasonable assumptions when data is restricted to a subdomain, a challenge explained through a Hardy-Hodge decomposition of spherical vector fields.
This paper establishes the Drinfeld correspondence between Poisson Lie groups and Lie bialgebras in the infinite-dimensional setting, specifically extending the theory to regular Lie groups modeled on convenient vector spaces such as nuclear Fréchet and Silva spaces, with applications to loop groups and diffeomorphism groups.