Fitouhi, A.; Dhaouadi, L.; Karoui, I. On the Bessel-Wright transform. (English) Zbl 1438.33026 Anal. Math. 45, No. 2, 291-309 (2019). 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. Cited in 2 ReviewsCited in 3 Documents MSC: 33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\) 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) Keywords:Bessel-Wright function; Bessel-Wright transform; Hardy transform; Lommel function; Bessel-Fourier transform PDFBibTeX XMLCite \textit{A. Fitouhi} et al., Anal. Math. 45, No. 2, 291--309 (2019; Zbl 1438.33026) Full Text: DOI