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Paley-Wiener-type theorem for a class of integral transforms arising from a singular Dirac system. (English) Zbl 0970.44003

A Paley-Wiener-type theorem giving a characterization of weighted \(L_2(I)\) spaces in terms of their images under various integral transforms is established, where \(I\) is a finite interval. As examples, the Hartley and some other transforms with the Airy and the Bessel function as kernels are derived, and the Paley-Wiener theorem is obtained for these transforms. The class of integral transformations considered herein is related to certain singular Dirac systems on a half line.
Reviewer: K.C.Gupta (Jaipur)

MSC:

44A15 Special integral transforms (Legendre, Hilbert, etc.)
34B24 Sturm-Liouville theory
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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References:

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