Orthonormal polynomial basis in local Dirichlet spaces
We provide an orthogonal basis of polynomials for the local Dirichlet space Dζ . These polynomials have numerous interesting features and a very unique algebraic pattern. We obtain the recurrence relation, the generating function, a simple formula for their norm, and explicit formulae for the distan...
Elmentve itt :
| Szerzők: | |
|---|---|
| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2021
|
| Sorozat: | Acta scientiarum mathematicarum
87 No. 3-4 |
| Kulcsszavak: | Dirichlet-tér, Analízis - matematikai |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-021-465-4 |
| Online Access: | http://acta.bibl.u-szeged.hu/75857 |
| Tartalmi kivonat: | We provide an orthogonal basis of polynomials for the local Dirichlet space Dζ . These polynomials have numerous interesting features and a very unique algebraic pattern. We obtain the recurrence relation, the generating function, a simple formula for their norm, and explicit formulae for the distance and the orthogonal projection onto the subspace of polynomials of degree at most n. The latter implies a new polynomial approximation scheme in local Dirichlet spaces. Orthogonal polynomials in a harmonically weighted Dirichlet space, created by a finitely supported singular measure, are also studied. |
|---|---|
| Terjedelem/Fizikai jellemzők: | 595-613 |
| ISSN: | 2064-8316 |