69 papers
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 establishes the almost sure Hausdorff dimension of the images and graphs of a broad class of random complex series, which encompasses famous deterministic functions like the Weierstrass and Riemann functions, thereby providing a probabilistic framework to predict the exact dimension values of their deterministic counterparts.
This paper establishes the existence of regular global and exponential attractors with finite fractal dimension for the planar Coleman--Gurtin heat equation with memory and rough anisotropic diffusion encoded by a Beltrami coefficient, utilizing a combination of instantaneous smoothing techniques, maximal parabolic regularity, and quasiconformal estimates.
This paper investigates the convergence properties of M.V. Berry's superoscillating approximation to the truncated Weierstrass function, providing sharp error estimates and analyzing the associated double limits.
This paper establishes a new Morales-Ramis type theorem for the meromorphic Jacobi non-integrability of general analytic dynamical systems by linking Jacobian multipliers to Lie algebra structures, and applies this criterion to analyze the polynomial integrability of Karabut systems modeling stationary gravity waves.
This paper proves and generalizes Z.-W. Sun's conjectures on infinite series involving harmonic numbers and binomial coefficients by evaluating them in closed form through their interpretation as automorphic objects on the moduli spaces of Legendre curves with genera 1, 2, 3, and 5.
This paper establishes a new global endpoint Sobolev inequality for measures that extends the Meyers-Ziemer theorem by incorporating a maximal function, thereby unifying and advancing the understanding of weighted bounded variation, isoperimetric inequalities, and fractional operator estimates while identifying sharp conditions for non-endpoint cases.
This paper establishes and proves the sharpness of a Newman bound counterpart for the Chui conjecture regarding Coulomb potentials generated by positive charges on the boundary of a unit ball, while also discussing a related problem involving charges within the unit disc.
This paper demonstrates that Riesz energies with exponents differing by one emerge as the limiting cases of a one-parameter family of infinite-strip energies under Neumann boundary conditions as the strip thickness varies from zero to infinity, offering a potential approach to a capacity conjecture by Pólya and Szegő.
This paper derives new elliptic integral identities by embedding Coxeter's classical integrals into a one-parameter family, differentiating with respect to the parameter to express the result in terms of incomplete elliptic integrals, and integrating back to establish a direct connection between Coxeter's original evaluations and elliptic functions.
This paper proves that a function penalizing deviations from equilibrium is uniquely determined as the "canonical reciprocal cost" (the difference between arithmetic and geometric means of a ratio and its reciprocal) by combining a d'Alembert-type composition law with a single quadratic calibration, while also demonstrating the necessity of these assumptions for uniqueness and establishing stability properties.
This paper establishes the Hurwitz stability of Hurwitz-type matrix polynomials by deriving an explicit form of their associated Bezoutian and proposes an extension of this class to include polynomials formed by adding a non-Hurwitz-type polynomial to another.
This paper establishes sharp Fourier restriction estimates for certain degenerate higher codimensional quadratic surfaces by introducing a novel iterative broad-narrow analysis that overcomes the failure of rescaling invariance through a generalized Jacobian defined via algebraic and graph-theoretic tools.
This paper presents a complete solution to the infinite quantum signal processing problem for arbitrary Szegő functions by introducing the Riemann-Hilbert-Weiss algorithm, which provably computes individual phase factors independently and stably using polylogarithmic precision and polynomial computational cost.
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 sharp estimates for single-scale, full, and lacunary bilinear Nevo-Thangavelu spherical maximal operators on the Heisenberg group () by employing newly developed single-scale average estimates, Hopf's maximal ergodic theorem, and an adapted argument.
This paper establishes the asymptotic sharpness of a Nikolskii-type inequality for rational functions in the Wiener algebra by constructing explicit test functions that demonstrate the bound relating the Wiener norm to the -norm cannot be improved as the number of poles tends to infinity.
This paper demonstrates that while a continuous map into a metric space is of bounded variation if and only if its composition with every Lipschitz function is of bounded variation, this characterization fails for discontinuous maps in spaces like , infinite metric trees, and Laakso-type spaces, though it remains valid for ultrametric spaces without continuity assumptions.
This paper introduces the "little -function" as a degenerate limit of Zwegers' generalized -function, deriving it via -Borel summation of a divergent solution to the Ramanujan difference equation and establishing its key properties, including symmetries, connection formulas, and relations to -Fibonacci sequences and the Rogers-Ramanujan continued fraction.
This paper establishes dimension expansion results for -point configuration sets generated by real analytic functions, proving that such sets attain positive Lebesgue measure or strictly larger Hausdorff dimensions under specific conditions by leveraging optimal -based Sobolev estimates for Fourier integral operators and extending the Mattila-Sjölin and Falconer-type frameworks.