Wavelets and generalized windowed transforms associated with the Dunkl-Bessel-Laplace operator on \(\mathbb{R}^d \times \mathbb{R}_{+}\) (Q892129)
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scientific article; zbMATH DE number 6510995
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Wavelets and generalized windowed transforms associated with the Dunkl-Bessel-Laplace operator on \(\mathbb{R}^d \times \mathbb{R}_{+}\) |
scientific article; zbMATH DE number 6510995 |
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Wavelets and generalized windowed transforms associated with the Dunkl-Bessel-Laplace operator on \(\mathbb{R}^d \times \mathbb{R}_{+}\) (English)
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18 November 2015
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The authors describe some properties of the Dunkl-Bessel-Laplace operator \(\Delta_{k,\beta}\) which is a special partial differential-difference operator. Corresponding to \(\Delta_{k,\beta}\), a translation operator and a convolution is introduced. For the Dunkl-Bessel transform, an inversion formula and a Plancherel-type theorem are presented. Associated with \(\Delta_{k,\beta}\), Gaussian wavelets are constructed.
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Dunkl-Bessel-Laplace operator
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partial differential-difference operator
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translation operator
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convolution
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Dunkl-Bessel transform
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Gaussian wavelets
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