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Paley–Wiener Theorems of Generalized Fourier Transform Associated with a Cherednik Type Operator on the Real Line

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Abstract

We consider a singular differential-difference operator \(\Lambda \) on the real line which generalizes the Cherednik operator associated with the reflection group \(\mathbb {Z}_2\) on \(\mathbb {R}\). We establish the Paley–Wiener theorems for the generalized Fourier transform on \(\mathbb {R}\) tied to \(\Lambda \).

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Acknowledgments

The author is deeply indebted to the referees and N-B. Andersen for their constructive comments and their helps in improving the contents of this paper. The author gratefully acknowledges the Deanship of Scientific Research at the Taibah University on the material and moral support.

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Authors and Affiliations

  1. Taibah University, College of Sciences, Department of Mathematics, 30001, Al Madinah Al Monawarah, Saudi Arabia

    Hatem Mejjaoli

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  1. Hatem Mejjaoli
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Correspondence to Hatem Mejjaoli.

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Communicated by Aad Dijksma.

This paper is dedicated to Professor Khalifa Trimèche on the occasion of his promotion to Professor Emeritus.

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Mejjaoli, H. Paley–Wiener Theorems of Generalized Fourier Transform Associated with a Cherednik Type Operator on the Real Line. Complex Anal. Oper. Theory 10, 1145–1170 (2016). https://doi.org/10.1007/s11785-015-0456-9

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  • DOI: https://doi.org/10.1007/s11785-015-0456-9

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