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Orthogonal polynomials with a constant recursion formula and an application to harmonic analysis. (English) Zbl 0549.43002
Le but de ce papier est le calcul de la mesure pour laquelle une suite de polynômes munie d’une formule de récurrence est orthogonale. Il généralise le cas des polynômes de Chebycheff en y adjoignant le théorème de translation de Christoffel, l’ensemble permettant d’obtenir les parties continue et discrète de la mesure. Les formules obtenues sont appliquées à des calculs d’analyse harmonique, en l’occurrence aux mesures sur la \(C^*\)-algèbre de certains groupes discrets ou finis. Les calculs sont présentés de façon complète, mais pour toutes les motivations et explications plus causales, les auteurs se contentent de renvois à des références.
Reviewer: P.Metzger

MSC:
43A05 Measures on groups and semigroups, etc.
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)
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