Orthonormal polynomial basis in local ...
Type de document :
Article dans une revue scientifique: Article original
URL permanente :
Titre :
Orthonormal polynomial basis in local Dirichlet spaces
Auteur(s) :
Fricain, Emmanuel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
Mashreghi, Javad [Auteur]
Université Laval [Québec] [ULaval]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
Mashreghi, Javad [Auteur]
Université Laval [Québec] [ULaval]
Titre de la revue :
Acta Scientiarum Mathematicarum
Pagination :
595-613
Éditeur :
Springer / Acta Universitatis Szegediensis
Date de publication :
2021
ISSN :
0001-6969
Mot(s)-clé(s) en anglais :
Harmonically weighted Dirichlet spaces
orthogonal polynomials polynomial
approximation
orthogonal polynomials polynomial
approximation
Discipline(s) HAL :
Mathématiques [math]
Résumé en anglais : [en]
We provide an orthogonal basis of polynomials for the local Dirichlet space $\mathcal D_\zeta$. These polynomials have numerous interesting features and a very unique algebraic pattern. We obtain the recurrence relation, ...
Lire la suite >We provide an orthogonal basis of polynomials for the local Dirichlet space $\mathcal D_\zeta$. 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.Lire moins >
Lire la suite >We provide an orthogonal basis of polynomials for the local Dirichlet space $\mathcal D_\zeta$. 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.Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
Projet ANR :
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Date de dépôt :
2025-01-24T14:59:02Z
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