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Discrete Fourier–Laplace Transforms of Lipschitz Functions in the Spaces \(S^{(p,q)}(\sigma ^{m-1})\)

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Abstract

In this paper, we extend the classical Titchmarsh theorem on the image under the discrete Fourier–Laplace transform of a set of functions satisfying a generalized Lipschitz and Dini–Lipschitz condition in the space \(S^{(p,q)}(\sigma ^{m-1})\), \(m\ge 3\). The given statements generalize the results of the author’s work published in El Ouadih and Daher (Integral Transforms Spec Funct 31(12):1010–1019, 2020).

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Acknowledgements

The author is grateful to the referees for the useful comments and suggestions in improving the presentation of the paper.

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Authors and Affiliations

  1. Laboratory MC, Polydisciplinary Faculty of Safi, Cadi Ayyad University, Marrakech, Morocco

    S. El Ouadih

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  1. S. El Ouadih
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Correspondence to S. El Ouadih.

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Communicated by Daniel Aron Alpay.

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This article is part of the topical collection “Harmonic Analysis and Operator Theory” edited by H. Turgay Kaptanoglu, Aurelian Gheondea and Serap Oztop.

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El Ouadih, S. Discrete Fourier–Laplace Transforms of Lipschitz Functions in the Spaces \(S^{(p,q)}(\sigma ^{m-1})\). Complex Anal. Oper. Theory 15, 69 (2021). https://doi.org/10.1007/s11785-021-01117-3

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  • DOI: https://doi.org/10.1007/s11785-021-01117-3

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