Namias' fractional Fourier transforms on \(L^ 2\) and applications to differential equations (Q1122735)
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scientific article; zbMATH DE number 4107386
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Namias' fractional Fourier transforms on \(L^ 2\) and applications to differential equations |
scientific article; zbMATH DE number 4107386 |
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Namias' fractional Fourier transforms on \(L^ 2\) and applications to differential equations (English)
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1988
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A fractional Fourier transform \(F_{\alpha}\), \(\alpha\in R\), earlier considered formally by \textit{V. Namias} [J. Inst. Math. Appl. 25, 241-265 (1980; Zbl 0434.42014)] is investigated in the space \(L^ 2(R)\). It is proved that \(\{F_{\alpha},\alpha \in R\}\) is a strongly continuous unitary group of operators on \(L^ 2(R)\). Applications to the solution of partial differential equations are added.
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fractional Fourier transform
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