Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/4587
Title: Hardy-type theorem for orthogonal functions with respect to their zeros. The Jacobi weight case
Authors: Abreu, L. D. 
Marcellan, F. 
Yakubovich, S. B. 
Keywords: Zeros of special functions; Orthogonality; Jacobi weights; Mellin transform on distributions; Entire functions; Bessel functions; Hyperbessel functions
Issue Date: 2008
Keywords: Zeros of special functions; Orthogonality; Jacobi weights; Mellin transform on distributions; Entire functions; Bessel functions; Hyperbessel functions
Issue Date: 2008
Citation: Journal of Mathematical Analysis and Applications. 341:2 (2008) 803-812
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 [lambda]n, , 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)=z[nu]F(z), , where F is entire and when n[not equal to]m. Considering all possible functions on this class we obtain a new family of generalized Bessel functions including Bessel and hyperbessel functions as special cases.
URI: http://hdl.handle.net/10316/4587
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Internacionais

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