Index transforms associated with Bessel and Lommel functions
type: Item
instance of: scholarly article
title: Index transforms associated with Bessel and Lommel functions
zbMATH Open document ID: 1013.44003
DOI: 10.4171/ZAA/1099
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2003-07-02T00:00:00Z
review text: The author extends a variety of index transforms with Bessel and Lommel functions as kernels by considering mapping properties of the related integral operators. The integral representations of the considered kernels are deduced. Boundedness properties of Lommel and Bessel function transforms are discussed. Parseval equalities, Plancherel type theorems and inversion formulas are also given. Actually this work is in continuation of the author's previous works, interested research workers of this field may also see the following monograph and papers of the author: Index transforms (1996; Zbl 0845.44001); J. Comput. Appl. Math. 85, No. 1, 169-179 (1997; Zbl 0886.44003); ibid. 118, No. 1-2, 353-361 (2000; Zbl 0959.44005).
Mathematics Subject Classification ID: 44A20
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 33C05
Mathematics Subject Classification ID: 33E20
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 1827602
zbMATH Keywords: Macdonald and hypergeometric functions
zbMATH Keywords: index transforms
zbMATH Keywords: Lommel functions
zbMATH Keywords: Bessel function transforms
zbMATH Keywords: Parseval equalities
zbMATH Keywords: Plancherel type theorems
zbMATH Keywords: inversion formulas
author: S. Yakubovich
reviewed by: H. S. P. Shrivastava
MaRDI profile type: Publication
cites work: Q5824493
cites work: Q3999269
cites work: Q3141895
cites work: Q5769133
cites work: Q5846853
cites work: Index integral transformations of Titchmarsh type
cites work: The Titchmarsh integral transformation by the index of a Bessel function
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description: scientific article; zbMATH DE number 1827602