Fricain Emmanuel and Mashreghi Javad: Orthonormal polynomial basis in local Dirichlet spaces. In: Acta scientiarum mathematicarum, (87) 3-4. pp. 595-613. (2021)
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Abstract
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.
| Item Type: | Article |
|---|---|
| Heading title: | Analysis |
| Journal or Publication Title: | Acta scientiarum mathematicarum |
| Date: | 2021 |
| Volume: | 87 |
| Number: | 3-4 |
| ISSN: | 2064-8316 |
| Page Range: | pp. 595-613 |
| Language: | English |
| Place of Publication: | Szeged |
| Related URLs: | http://acta.bibl.u-szeged.hu/75796/ |
| DOI: | 10.14232/actasm-021-465-4 |
| Uncontrolled Keywords: | Dirichlet-tér, Analízis - matematikai |
| Additional Information: | Bibliogr.: p. 611-613. ; összefoglalás angol nyelven |
| Subjects: | 01. Natural sciences 01. Natural sciences > 01.01. Mathematics |
| Date Deposited: | 2022. May. 24. 13:39 |
| Last Modified: | 2022. May. 24. 13:39 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/75857 |
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