Orthonormal polynomial basis in local Dirichlet spaces

Fricain, Emmanuel; Mashreghi, Javad

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.14232/actasm-021-465-4

Title :

Orthonormal polynomial basis in local Dirichlet spaces

Author(s) :

Fricain, Emmanuel [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
Mashreghi, Javad [Auteur]
Université Laval [Québec] [ULaval]

Journal title :

Acta Scientiarum Mathematicarum

Pages :

595-613

Publisher :

Springer / Acta Universitatis Szegediensis

Publication date :

2021

ISSN :

0001-6969

English keyword(s) :

Harmonically weighted Dirichlet spaces
orthogonal polynomials polynomial
approximation

HAL domain(s) :

Mathématiques [math]

English abstract : [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, ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Frontières de la théorie des opérateurs

Collections :