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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 3, 2002, pp. 627–638
DOI: 10.4171/ZAA/1099

Published online: 2002-09-30

Index Transforms Associated with Bessel and Lommel Functions

Semyon B. Yakubovich[1]

(1) Faculdade de Ciências do Porto, Portugal

In this paper we extend a variety of index integral transforms (i.e. integral transforms over an index as integration variable) with Bessel and Lommel functions as kernels by considering mapping properties of the related integral operators. This class of transforms includes, for instance, operators of Titchmarsh type. Useful integral representations of the considered kernels are deduced and boundedness properties, Parseval equalities, Plancherel type theorem and inversion formula are given.

Keywords: Lommel, Bessel, Macdonald and hypergeometric functions; Mellin, Kontorovich- Lebedev, Fourier cosine and sine transforms; Parseval equality, Plancherel theorem

Yakubovich Semyon: Index Transforms Associated with Bessel and Lommel Functions. Z. Anal. Anwend. 21 (2002), 627-638. doi: 10.4171/ZAA/1099