Hardy-type theorem for orthogonal functions with respect to their zeros. The Jacobi weight case

• Autor(a) principal: Abreu, L. D.
• Data de Publicação: 2008
• Outros Autores: Marcellán, F., Yakubovich, S. B.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/4587; https://doi.org/10.1016/j.jmaa.2007.10.050
• topic: Zeros of special functions; Orthogonality; Jacobi weights; Mellin transform on distributions; Entire functions; Bessel functions; Hyperbessel functions

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.