The reproducing kernel structure arising from a combination of continuous and discrete orthogonal polynomials into Fourier systems
| dc.creator | Abreu, Luis Daniel | |
| dc.date | 2006-01-09 | |
| dc.date | 2007-01-05 | |
| dc.date.accessioned | 2026-07-07T07:38:33Z | |
| dc.date.available | 2026-07-07T07:38:33Z | |
| dc.description | We study mapping properties of operators with kernels defined via a combination of continuous and discrete orthogonal polynomials, which provide an abstract formulation of quantum (q-) Fourier type systems. We prove Ismail conjecture regarding the existence of a reproducing kernel structure behind these kernels, by establishing a link with Saitoh theory of linear transformations in Hilbert space. The results are illustrated with Fourier kernels with ultraspherical weights, their continuous q-extensions and generalizations. As a byproduct of this approach, a new class of sampling theorems is obtained, as well as Neumann type expansions in Bessel and q-Bessel functions. | |
| dc.description | 16 pages; Title changed, major reformulations. To appear in Constr. Approx | |
| dc.identifier | https://arxiv.org/abs/math/0601190 | |
| dc.identifier | http://arxiv.org/abs/math/0601190 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121126 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 42C15; 44A20; 33C45; 33D45; 94A20 | |
| dc.title | The reproducing kernel structure arising from a combination of continuous and discrete orthogonal polynomials into Fourier systems | |
| dc.type | text |