On the Bessel–Wright Transform

In the present paper, we consider a class of second-order singular differential operators which generalize the well-known Bessel differential operator. The associated eigenfunctions are the Bessel–Wright functions. These functions can be obtained by the action of the Riemann–Liouville operator on th...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) 2019-06, Vol.45 (2), p.291-309
Main Authors: Fitouhi, A., Dhaouadi, L., Karoui, I.
Format: Article
Language:English
Subjects:
Analysis
Bessel functions
Differential equations
Eigenvectors
Fourier transforms
Mathematics
Mathematics and Statistics
Metric space
Operators (mathematics)
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Summary:In the present paper, we consider a class of second-order singular differential operators which generalize the well-known Bessel differential operator. The associated eigenfunctions are the Bessel–Wright functions. These functions can be obtained by the action of the Riemann–Liouville operator on the normalized Bessel functions. We introduce a Bessel–Wright transform with Bessel–Wright functions as kernel which is connected to the classical Bessel–Fourier transform via the dual of the Riemann–Liouville operator. The Bessel–Wright transform leaves invariant the Schwartz space and sends the set of functions indefinitely differentiable with compact support into the Paley–Wiener space. We conclude the paper by proving two variants of the inversion formulas.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-018-0659-1