Convolutions and integral equations weighted by multi-dimensional Hermite functions

DOI10.1142/S1793557122501510zbMath1506.45004MaRDI QIDQ5876772

Rita C. Guerra, Nguyen Minh Tuan, Luis Filipe Pinheiro de Castro

Publication date: 2 February 2023

Published in: Asian-European Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

integral equationconvolutionHermite functionYoung's inequalitynormed ringWiener's algebra

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Integral transforms of special functions (44A20) Linear operators on Banach algebras (47B48) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Other transforms and operators of Fourier type (43A32) Rings and algebras of continuous, differentiable or analytic functions (46E25)

Cites Work

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• The Hermite functions related to infinite series of generalized convolutions and applications
• The solvability and explicit solutions of two integral equations via generalized convolutions
• Harmonic analysis on the Heisenberg group
• The finite Hartley new convolutions and solvability of the integral equations with Toeplitz plus Hankel kernels
• New convolutions and norm inequalities
• Mapping Properties and Composition Structure of Multidimensional Integral Transforms
• Regularity of convolution type operators with PC symbols in Bessel potential spaces over two finite intervals
• A class of integral transforms related to the fourier cosine convolution
• New convolutions weighted by Hermite functions and their applications

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