Espaces de séries de Dirichlet et leurs opérateurs de composition

Queffélec, Hervé

Annales mathématiques Blaise Pascal, Numéro spécial Ecole de Printemps d’Analyse, Tome 22 (2015) no. S2, pp. 267-344.

Ce survol est divisé en trois chapitres : le premier porte sur les propriétés générales des séries de Dirichlet ${\sum }_{n=1}^{\infty }{a}_n{n}^{-s}$ et de leur somme, et présente le point de vue de Bohr (relèvement). Le second étudie les espaces de Hardy-Dirichlet de telles séries sur un demi-plan vertical, avec une application aux systèmes de Riesz. Le troisième enfin porte sur les opérateurs de composition agissant sur ces espaces et leurs nombres d’approximation. Le comportement de ces nombres se révèle assez différent de ceux rencontrés dans le cas des espaces de Hardy classiques.

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