Journal
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS
Volume 11, Issue 4, Pages 1685-1697Publisher
SPRINGER BASEL AG
DOI: 10.1007/s11868-020-00368-6
Keywords
Fourier-Jacobi expansion; Fourier-Jacobi transform; Generalized translation operator; Lipschitz class; Titchmarsh theorem
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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 Lipschitz functions on compact groups, Ph.D. Thesis, McMaster University, Hamilton, Ontario, Canada, 1974, Theorem 2.6) on the image under the discrete Fourier-Jacobi transform of a set of functions satisfying a generalized Lipschitz condition in the weighted spaces L-p([0,pi]), 1 <= 2. For this purpose, we use a generalized translation operator which was defined by Flensted-Jensen and Koornwinder in (The convolution structure for Jacobi function expansions, Ark. Mat., 1973)
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