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Discrete Fourier-Jacobi Transform and Generalized Lipschitz Classes
El Mehdi Loualid
,
Abdelghani Elgargati
,
Radouan Daher
Abstract
In this paper, we use the methods of Fourier-Jacobi harmonic analysis to generalize Boas-type results. We give necessary and sufficient conditions in terms of the Fourier-Jacobi coefficients of a function $f$ in order to ensure that it belongs either to one of the generalized Lipschitz classes ${H}_{\alpha }^{m}$ and ${h}_{\alpha }^{m}$ for $\alpha > 0$.