Paley–Wiener and Boas theorems for singular Sturm–Liouville integral transforms |
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Authors: | Vu Kim Tuan |
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Affiliation: | Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, PO Box 5969, Safat 13060, Kuwait |
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Abstract: | This paper deals with a class of integral transforms arising from a singular Sturm–Liouville problem y″−q(x)y=−λy, x(a,b), in the limit-point case at one end or both ends of the interval (a,b). The paper completely solves the problem of characterization of the image of a function that has compact support (Paley–Wiener theorem) and also of a function that vanishes on some interval (Boas problem) under this class of transforms. The characterizations are obtained with no restriction on q(x) other than being locally integrable. |
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Keywords: | Paley– Wiener theorem Boas theorem Singular Sturm– Liouville problems Eigenfunction expansions Finite integral transforms Hankel transform |
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