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Paley-Wiener-type theorems for a class of integral transforms. (English) Zbl 0998.44001
In this interesting paper the authors give a characterization of weighted \(L_2 (I)\) spaces in terms of their images under several integral transforms. These findings are then used to derive Paley-Wiener type theorems for these spaces. The results obtained here use real variable techniques and do not require analytic continuation to the complete plane.
Eight examples involving various integral transforms are considered. They involve singular Sturm-Liouville boundary-value problems on a half line and on the whole line.
The approach considered herein is indeed unified in nature and covers a large spectrum of integral transforms.
Reviewer: K.C.Gupta (Jaipur)

MSC:
44A05 General integral transforms
34B24 Sturm-Liouville theory
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