Ce survol est divisé en trois chapitres : le premier porte sur les propriétés générales des séries de Dirichlet 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.
@article{AMBP_2015__22_S2_267_0, 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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