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Hardy-type theorem for orthogonal functions with respect to their zeros. The Jacobi weight case |
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| Authors: | LD Abreu F Marcellan SB Yakubovich |
| Institution: | a Department of Mathematics, FCTUC, University of Coimbra, 3001-454 Coimbra, Portugal b NuHag, Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Wien, Austria c Department of Mathematics, University Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain d Department of Pure Mathematics, Faculty of Sciences, University of Porto, Campo Alegre st., 687, 4169-007 Porto, Portugal |
| Abstract: | Motivated by the G.H. Hardy's 1939 results G.H. Hardy, Notes on special systems of orthogonal functions II: On functions orthogonal with respect to their own zeros, J. London Math. Soc. 14 (1939) 37-44] on functions orthogonal with respect to their real zeros λn,  , we will consider, under the same general conditions imposed by Hardy, functions satisfying an orthogonality with respect to their zeros with Jacobi weights on the interval (0,1), that is, the functions f(z)=zνF(z), ν∈R, where F is entire and |
| Keywords: | Zeros of special functions Orthogonality Jacobi weights Mellin transform on distributions Entire functions Bessel functions Hyperbessel functions |
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