RT Journal Article
T1 Hardy-type theorem for orthogonal functions with respect to their zeros. The Jacobi weight case
A1 Abreu, L. D.
A1 Marcellán Español, Francisco José
A1 Yakubovich, S. B.
AB 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, n=1,2,... , 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^ν F(z), ν in R, where F is entire and,
AB $\int_0 1 f(λ_n t)f(λ_m t)t (1-t) dt=0, α>-1-2ν, β>-1
AB when n≠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.
PB Elsevier
SN 0022-247X
YR 2008
FD 2008-05-15
LK https://hdl.handle.net/10016/5916
UL https://hdl.handle.net/10016/5916
LA eng
NO 10 pages, no figures.
NO MR#: MR2398249 (2009d:46074)
NO Zbl#: Zbl 1139.42005
NO The work of LDA has been supported by CMUC and FCT post-doctoral grant SFRH/BPD/26078/2005. The work of FM has been supported by Dirección General de Investigación, Ministerio de Educación y Ciencia of Spain, MTM 2006-13000-C03-02. The work of SBY has been supported, in part, by the "Centro de Matemática" of the University of Porto.
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RD 24 jun. 2024