Espaces de séries de Dirichlet et leurs opérateurs de composition

Hervé Queffélec

doi:10.5802/ambp.351

Hervé Queffélec

Annales Mathématiques Blaise Pascal, Tome 22 (2015) no. S2, pp. 267-344.

Résumé

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.

DOI : https://doi.org/10.5802/ambp.351
Classification : 47B33, 30B50, 30H10
Mots clés: Dirichlet series, Composition operators, Approximation numbers

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     author = {Herv\'e Queff\'elec},
     title = {Espaces de s\'eries de Dirichlet et leurs op\'erateurs de composition},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {267--344},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {22},
     number = {S2},
     year = {2015},
     doi = {10.5802/ambp.351},
     language = {fr},
     url = {ambp.centre-mersenne.org/item/AMBP_2015__22_S2_267_0/}
}

Hervé Queffélec. Espaces de séries de Dirichlet et leurs opérateurs de composition. Annales Mathématiques Blaise Pascal, Tome 22 (2015) no. S2, pp. 267-344. doi : 10.5802/ambp.351. https://ambp.centre-mersenne.org/item/AMBP_2015__22_S2_267_0/

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