Pointwise convergence of fractional powers of Hermite type operators

DOI10.33044/revuma.4357zbMath1527.35136arXiv2211.06359OpenAlexW4386927338MaRDI QIDQ6070529

Beatriz E. Viviani, Guillermo J. Flores, Teresa Signes, Gustavo Garrigós

Publication date: 23 November 2023

Published in: Revista de la Unión Matemática Argentina (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.06359

zbMATH Keywords

fractional LaplacianHermite operatorPoisson integralsOrnstein-Uhlenbeck semigroup

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Integral representations of solutions to PDEs (35C15) Convergence and divergence of integrals (40A10) Fractional partial differential equations (35R11)

Cites Work

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• Ten equivalent definitions of the fractional Laplace operator
• Regularity theory for the fractional harmonic oscillator
• On the pointwise convergence to initial data of heat and Poisson problems for the Bessel operator
• A.e. convergence and 2-weight inequalities for Poisson-Laguerre semigroups
• Pointwise convergence to initial data of heat and Laplace equations
• Fractional Laplacian on the torus
• Extension Problem and Harnack's Inequality for Some Fractional Operators
• A weak 2-weight problem for the Poisson-Hermite semigroup
• An Extension Problem Related to the Fractional Laplacian
• HERMITE FUNCTION EXPANSIONS VERSUS HERMITE POLYNOMIAL EXPANSIONS
• A Calderón theorem for the Poisson semigroups associated with the Ornstein-Uhlenbeck and Hermite operators