Hardy-type theorem for functions orthogonal with respect to their zeros. The Jacobi weight case
| dc.creator | Abreu, L. D. | |
| dc.creator | Marcellan, F. | |
| dc.creator | Yakubovich, S. | |
| dc.date | 2007-01-05 | |
| dc.date.accessioned | 2026-07-07T07:38:51Z | |
| dc.date.available | 2026-07-07T07:38:51Z | |
| dc.description | Motivated by G. H. Hardy's 1939 results \cite{Hardy} on functions orthogonal with respect to their real zeros $λ_{n}, n=1,2,... $, we will consider, within 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 $f(z)=z^νF(z), ν\in \mathbb{R}$, where $F$ is entire and \begin{equation*} \int_{0}^{1}f(λ_{n}t)f(λ_{m}t)t^α(1-t)^βdt=0,\quad α>-1-2ν, β>-1, \end{equation*}% when $n\neq m$. Considering all possible functions on this class we are lead to the discovery of a new family of generalized Bessel functions including Bessel and Hyperbessel functions as special cases. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701175 | |
| dc.identifier | http://arxiv.org/abs/math/0701175 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121244 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.title | Hardy-type theorem for functions orthogonal with respect to their zeros. The Jacobi weight case | |
| dc.type | text |