125 papers
This paper provides the first systematic treatment of the measure-theoretic properties of nonlinear Lebesgue spaces, unifying scattered literature results and extending classical theorems on completeness, separability, and the density of simple, continuous, and smooth mappings to this broader nonlinear framework.
This paper computes Raja's covering index for infinite-dimensional Hilbert spaces, establishes sharp asymptotic estimates for scalar-valued spaces under renormability conditions, provides uniform upper bounds for Bochner spaces that partially resolve a question by Raja, and derives power-type lower bounds for non-commutative spaces using non-commutative Clarkson inequalities.
This paper extends fractional linear transformations from Banach algebras to general rings via Wedderburn's continued fractions, establishing a connection to the projective elementary group PE(2,R) to define a length function and prove structural results regarding the perfectness and simplicity of its commutator subgroup.
This paper constructs and evaluates compactly supported dual Gabor windows generated by B-splines and exponential B-splines, demonstrating through signal and image reconstruction experiments that these windows offer stable, computationally efficient alternatives to canonical duals for practical applications.
This paper introduces spectral Barron spaces within the framework of quantum harmonic analysis, establishes their fundamental properties such as completeness and continuous embeddings, and applies these results to prove the existence and uniqueness of solutions for a Schrödinger-type equation.
This paper classifies and analyzes exactly solvable one-dimensional complex Schrödinger operators related to the Gauss hypergeometric equation, organizing them into three geometric families (spherical, hyperbolic, and deSitterian) to compute their spectra and Green functions while establishing transmutation identities and linking them to symmetric manifolds.
This paper establishes necessary and sufficient conditions for the compactness of the embedding on the half-space with general singular weights, proving that compactness holds if and only if the measure has finite mass and satisfies a global tightness condition characterized by coercive tail inequalities and, in singular cases, weighted Hardy inequalities.
This paper defines a speed measure for locally bounded variation curves in metric spaces, characterizes their continuity and absolute continuity through this measure, identifies its Radon-Nikodým derivative as the metric speed, and establishes an extension of the Banach-Zaretsky theorem.
This paper extends Suzuki's approach to Kannan and Chatterjea type contractions by utilizing the CJM condition to establish the weakest possible conditions that ensure the convergence of all Picard sequences to a fixed point, thereby proving the optimality of these conditions.
This paper establishes a conformal scattering theory for defocusing semilinear wave equations on Schwarzschild spacetime by combining energy decay estimates with Sobolev embeddings to construct a bounded, locally Lipschitz scattering operator that maps past to future scattering data.
This paper establishes a real version of the Lax-Phillips Theorem and classifies outgoing reflection positive orthogonal one-parameter groups to derive a normal form for outgoing monotone geodesics in the set of standard subspaces, utilizing explicit symbols for positive Hankel operators to distinguish these geodesics from those arising in Borchers' Theorem.
This paper characterizes the Legendre, Laplace, and identity transforms as the unique continuous, contravariant valuations with specific conjugation or duality properties on spaces of convex and log-concave functions.
This paper investigates two-variable compressions of shifts associated with rational inner functions on the bidisk, establishing their unitary equivalence to matrix-valued Toeplitz operators and demonstrating that while these symbols almost uniquely determine the underlying functions, the numerical ranges of the compressed shifts do not.
This paper establishes Banach, Newton-Raphson, and Brouwer fixed point theorems within the framework of generalized smooth functions, thereby enabling the rigorous solution of nonlinear singular equations involving distributions that fall outside the scope of classical fixed point theory.
This paper characterizes the spectrum of Hausdorff operators acting on weighted Bergman and power weighted Hardy spaces defined over the upper half-plane.
This paper establishes a new pointwise estimate for rough operators in Ahlfors regular metric measure spaces by combining a subrepresentation formula involving modified Riesz potentials with a maximal function control, and subsequently derives a family of functional inequalities from this result.
This paper introduces a new family of -Berezin seminorms to establish refined inequalities for the Berezin radius and investigates the convexity of Berezin ranges for specific operators on weighted Hardy and Fock spaces.
This paper establishes that the asymptotic accumulation of eigenvalues near unity for convolutions of indicator functions and density operators on locally compact groups occurs if and only if the group is unimodular and the underlying sets form a Følner sequence, thereby extending known results for the Heisenberg group to broader classes such as nilpotent and homogeneous Lie groups.
This paper establishes the foundational theory of covers and envelopes within proto-exact categories and applies these results to prove that categories of Banach modules over arbitrary Banach rings possess enough injectives.
This paper establishes a measure-theoretic framework for constructing Arveson systems from stationary factorizing measure types, providing a rigorous characterization of spatiality and a robust mechanism for generating type III systems via infinite products, which is applied to derive explicit type III random-set systems from the zero sets of Brownian motion.