Square summability with geometric weight for classical orthogonal expansions
| dc.creator | Karp, D. | |
| dc.date | 2006-04-03 | |
| dc.date.accessioned | 2026-07-07T07:10:25Z | |
| dc.date.available | 2026-07-07T07:10:25Z | |
| dc.description | Let $f_k$ be the $k$-th Fourier coefficient of a function $f$ in terms of the orthonormal Hermite, Laguerre or Jacobi polynomials. We give necessary and sufficient conditions on $f$ for the inequality $\sum_{k}|f_k|^2θ^k<\infty$ to hold with $θ>1$. As a by-product new orthogonality relations for the Hermite and Laguerre polynomials are found. The basic machinery for the proofs is provided by the theory of reproducing kernel Hilbert spaces. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0604028 | |
| dc.identifier | http://arxiv.org/abs/math/0604028 | |
| dc.identifier | Advances in Analysis, Proceedings of the 4th International ISAAC Conference (H. G. W. Begehr et al, eds.), World Scientific, Singapore-NewJersey-London, 2005, 407-421 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111418 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 30B40, 46E22 | |
| dc.title | Square summability with geometric weight for classical orthogonal expansions | |
| dc.type | text |