Equivalence of the Weighted Fractional Sobolev Space on a Disk with Characterization by the Decay Rate of Fourier–Jacobi Coefficients and K-Interpolation
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DOI: 10.1007/s00041-024-10127-6
Abstract: In this paper, motivated by the analysis of the fractional Laplace equation on the unit disk in R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^{2}$$\end{document}, we establish a characterisation of the weighted… read more here.
Keywords: sobolev space; decay rate; rate fourier; fourier jacobi ... See more keywords
Weighted approximation for the generalized discrete Fourier–Jacobi transform on space $$L_{p}({\mathbb {T}})$$
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DOI: 10.1007/s11868-020-00368-6
Abstract: The purpose of this work is to prove an analog of the classical Titchmarsh’s theorem (Introduction to the theory of Fourier integrals, Oxford University Press, Oxford, 1937, Theorem 84) and Younis’s Theorem (Fourier transform of… read more here.
Keywords: weighted approximation; jacobi; fourier jacobi; jacobi transform ... See more keywords
Integrability of the Fourier–Jacobi transform of functions satisfying Lipschitz and Dini–Lipschitz-type estimates
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DOI: 10.1080/10652469.2021.1913414
Abstract: ABSTRACT The purpose of this work is to prove analogues of the classical Titchmarsh theorem and Younis' theorem associated with the Fourier–Jacobi transform of a set of functions satisfying a generalized Lipschitz condition of a… read more here.
Keywords: integrability fourier; jacobi transform; functions satisfying; fourier jacobi ... See more keywords
Harmonic analysis associated with the linear canonical Fourier–Jacobi transform
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DOI: 10.1080/10652469.2024.2426183
Abstract: The main objective of this paper is to develop a new harmonic analysis related to a Fourier–Jacobi type operator $ \Delta _{\alpha,\beta }^m $ Δα,βm of the real line. We define and study the linear… read more here.
Keywords: jacobi transform; canonical fourier; linear canonical; fourier jacobi ... See more keywords