Orthonormal polynomial basis in local Dirichlet spaces

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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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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