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Titchmarsh’s Theorem in Clifford Analysis

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Abstract

The Clifford Fourier transform (CFT) has been shown to be a crucial tool in the Clifford analysis. The purpose of this paper is to derive an analog of Titchmarsh’s theorems for the CFT for functions satisfying the Lipschitz and Dini–Lipschitz conditions in the space \(L^p(\mathbb {R}^{p,q},C\ell (p,q)), 1<p\le 2,\) where \(C\ell (p,q)\) is the Clifford algebra.

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Acknowledgements

The author would like to thank the editor and the reviewers for the interest they showed to the paper and for their constructive suggestions and comments. He further thanks R. Abłamowicz for very helpful comments that led to the improved presentation of the paper.

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  1. Equipe de Mathématiques Appliquées et Sciences de l’Information (MASI), Ecole Normale Supérieure (ENS-Meknès), University Moulay Ismail, 3104, Toulal, Meknès, Morocco

    Youssef El Haoui

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  1. Youssef El Haoui
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Correspondence to Youssef El Haoui.

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Communicated by Wolfgang Sprössig.

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El Haoui, Y. Titchmarsh’s Theorem in Clifford Analysis. Adv. Appl. Clifford Algebras 31, 10 (2021). https://doi.org/10.1007/s00006-020-01104-5

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  • DOI: https://doi.org/10.1007/s00006-020-01104-5

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