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...
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| Main Authors: | |
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| Format: | Article |
| Published: |
2021
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| Series: | Acta scientiarum mathematicarum
87 No. 3-4 |
| Kulcsszavak: | Dirichlet-tér, Analízis - matematikai |
| Subjects: | |
| doi: | 10.14232/actasm-021-465-4 |
| Online Access: | http://acta.bibl.u-szeged.hu/75857 |
| Summary: | 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. |
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| Physical Description: | 595-613 |
| ISSN: | 2064-8316 |