Absolutely convergent Fourier–Jacobi series and generalized Lipschitz classes. Issue 4 (3rd April 2023)

• Record Type: Journal Article
• Authors: Saadi, Faouaz; Daher, Radouan
• Is Part Of: Integral transforms and special functions. Volume 34:Issue 4(2023)
• Page Start: 334
• Page End: 345
• Publication Date: 2023-04-03
• Subjects: Fourier–Jacobi series -- Fourier–Jacobi transform -- generalized translation operator -- Lipschitz class -- Boas theorems; 43A30 -- 33D60; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2022.2122460
• Languages: English
• ISSNs: 1065-2469

Abstract

Abstract : In this paper, we give necessary and sufficient conditions in terms of Fourier–Jacobi coefficients of a function f, to ensure that f belongs either to one of the generalized Lipschitz classes H α, β m and h α, β m for α ≥ β ≥ − 1 / 2 and α ≠ − 1 / 2 . Also a condition for generalized Jacobi differentiability of a function on interval [ 0, π ] is proved.