Some integral transforms in the space of entire functions of exponential type (Q1924887)
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scientific article; zbMATH DE number 938084
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some integral transforms in the space of entire functions of exponential type |
scientific article; zbMATH DE number 938084 |
Statements
Some integral transforms in the space of entire functions of exponential type (English)
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4 December 1996
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An integral transformation is considered which has the confluent hypergeometric function \(\Phi_1\) in the kernel. This transformation provides an isomorphism in the space of entire functions of exponential growth. One of the special cases of interest involves Kummer's function, where the generalized Fourier kernel is \[ e^{i(x-y)} {_1F_1} \bigl[1+i \alpha,\;2+i \gamma;\;2i(y-x) \bigr]. \]
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confluent hypergeometric functions
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entire functions of exponential type
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Kummer's function
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generalized Fourier kernel
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