Index transforms associated with products of Whittaker's functions (Q1860455)
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scientific article; zbMATH DE number 1872894
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Index transforms associated with products of Whittaker's functions |
scientific article; zbMATH DE number 1872894 |
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Index transforms associated with products of Whittaker's functions (English)
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23 February 2003
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The author investigates several integral transformations with respect to parameters of the products of the Whittaker functions. In particular, a class of these transformations is shown to involve the Lebedev index transformation with the square of the Macdonald function. Boundedness and inversion properties are derived in the weighted \(L_2\)-spaces. The methods of Plancherel's theorems and Parseval's equalities for the Fourier, Mellin and Kontorovich-Lebedev transforms are also applied.
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boundedness
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Whittaker function
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Macdonald function
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Meijer \(G\)-function
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Fourier transform
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Mellin transform
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Kontorovich-Lebedev transform
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Parseval equality
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Lebedev index transformation
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inversion
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