125 papers
This paper establishes the continuum limit of a discrete Hodge-Dirac operator on -dimensional square lattices by introducing a novel higher-dimensional discrete differential calculus framework that generalizes standard simplicial complex methods and proves the operator's convergence to its continuous counterpart as the lattice spacing vanishes.
This paper characterizes the extreme and exposed points of the unit ball in the -norm for shift-invariant spaces generated by the Gaussian function and quasi shift-invariant spaces generated by the hyperbolic secant.
This paper establishes unweighted Hardy-type inequalities on step-two Carnot groups with one-dimensional vertical layers by employing a quantitative integration-by-parts mechanism that substitutes the non-horizontal Euler vector field with a controlled horizontal one, yielding explicit optimal constant bounds for the Heisenberg group and generalized non-isotropic structures.
This paper establishes that localization operators on weighted Bergman spaces converge weakly to those on Fock spaces under natural scaling as the parameter , a result leveraged to derive sharp norm estimates for Toeplitz operators, analyze windowed Berezin transforms, and prove Szegő-type theorems.
This paper establishes new refined lower and upper bounds for the numerical radius of bounded linear operators using Euclidean operator radius techniques, derives equality characterizations, and improves existing inequalities for operator commutators.
This paper investigates the functional analytic properties of "localized" locally convex topologies to characterize distributions arising as divergences of vector fields, demonstrating that while these topologies are sequential, they generally lack standard properties like being Fréchet-Urysohn or barrelled, and establishing a semireflexivity condition that yields a general existence theorem for solving .
This paper introduces and establishes the equivalence of various notions of boundedness and continuity for multilinear functionals and functions on n-normed spaces, demonstrating that these concepts yield identical dual spaces with equivalent norms while providing illustrative examples and exploring the relationship between bounded multilinear functionals and multicontinuous functions.
This paper characterizes the matrix polynomials and that satisfy a specific norm inequality and those for which the corresponding operator embedding is compact on bounded open sets.
This paper characterizes centered weighted composition operators on -spaces without assuming a product structure, introduces the concept of spectrally half-centered operators to analyze unbounded cases, and provides criteria for centered weighted shifts on directed trees of types I–IV.
This paper demonstrates that while order-preserving Lipschitz maps from subsets of one-dimensional partially ordered Hilbert spaces into Hadamard posets can always be extended without increasing the Lipschitz constant, such extensions are generally impossible in higher dimensions unless the order on the domain is trivial, thereby proving that no order-theoretic generalization of Kirszbraun's theorem exists.
This paper establishes Plancherel-type identities and proves the surjectivity of the Fourier transform for certain unbounded dual tiling sets in , demonstrating that an open set tiles the real line by the finite set if and only if it admits a spectrum given by the Lebesgue measure on .
This paper utilizes determinant representations of correlation functions in conformal field theory to derive explicit determinant formulas for powers of the classical -function via deformed elliptic functions, specifically obtaining counterparts of Garvan's formulas for the modular discriminant on genus two Riemann surfaces.
This paper establishes the continuity of derivations over a class of Banach algebras containing dense -like subalgebras, specifically demonstrating that every derivation on the -crossed product is continuous when the group is infinite, finitely generated, has polynomial growth, and acts freely on the compact Hausdorff space .
This paper extends the classical Kolmogorov-Riesz compactness theorem to asymptotic spaces on by proving that relative compactness in these nonlocally convex F-spaces is characterized by natural tail and translation conditions alongside a necessary additional almost equiboundedness requirement.
This paper refines moment comparison inequalities for sums of random vectors uniformly distributed on Euclidean spheres by establishing sharp constants and introducing an optimal deficit term, particularly in high dimensions.
This paper extends the classical sharp upper bound on central hyperplane sections of a regular simplex to a probabilistic framework involving negative moments of centered log-concave random variables, revealing a phase transition in the extremizing distributions for new sharp reverse Hölder-type inequalities.
This paper extends dilation results, characterizations, and decomposition theorems for operators in the class and quantum annulus to the setting of doubly commuting tuples of such operators.
This paper establishes a complete characterization of the compactness of Sobolev embeddings for radially symmetric functions on and weighted balls within the general framework of rearrangement-invariant function spaces by developing novel techniques that overcome the limitations of previous methods restricted to domains of finite measure.
This paper investigates the generalized Davis-Wielandt radius of Hilbert space operators by establishing new lower bounds for both this radius and the numerical radius, while also deriving an alternative to the triangular inequality for operators.
This paper establishes a comprehensive well-posedness theory for parabolic Cauchy problems with time-independent, uniformly elliptic, bounded measurable complex coefficients, demonstrating that tempered distributions in homogeneous Hardy–Sobolev or Besov spaces serve as valid initial data for weak solutions with gradients in weighted tent spaces when source terms are of Lions' type.