Continuity of the fractional Hankel wavelet transform on Gelfand-Shilov spaces
\textit{I. M. Gel'fand} and \textit{G. E. Shilov} [Generalized functions. Vol. I: Properties and operations. Translated by E. Saletan. New York, London: Academic Press (1964; Zbl 0115.33101)] introduced the notion of \(W\)-type spaces abreast of the properties of the Fourier transform on such spaces. As of now, the \(W\)-type spaces have found numerous applications in diverse aspects of science and engineering, particularly in the realm of partial differential operators. In this paper, the authors have examined the fractional Hankel wavelet transform on the Gelfand-Shilov spaces of type \(W\). To begin with, the authors have discussed some properties of the well-known fractional Hankel transform on certain \(W\)-type spaces. In the sequel, certain results regarding the continuity and boundedness properties of the fractional Hankel wavelet transform on a specific type of Gelfand-Shilov space are also presented.
scientific article; zbMATH DE number 7393813
scientific article