Convergence of Dirichlet polynomials in Banach spaces

[EN] Recent results on Dirichlet series Sigma(n) a(n) 1/n(s), s is an element of C, with coefficients a(n) in an infinite dimensional Banach space X show that the maximal width of uniform but not absolute convergence coincides for Dirichlet series and for m-homogeneous Dirichlet polynomials. But a c...

Descripción completa

Detalles Bibliográficos
Autores: Defant, Andreas, Sevilla Peris, Pablo|||0000-0001-5222-4768
Tipo de recurso: artículo
Fecha de publicación:2011
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/79781
Acceso en línea:https://riunet.upv.es/handle/10251/79781
Access Level:acceso abierto
Palabra clave:Vector valued
Dirichlet series
Dirichlet polynomials
Banach spaces
MATEMATICA APLICADA
Descripción
Sumario:[EN] Recent results on Dirichlet series Sigma(n) a(n) 1/n(s), s is an element of C, with coefficients a(n) in an infinite dimensional Banach space X show that the maximal width of uniform but not absolute convergence coincides for Dirichlet series and for m-homogeneous Dirichlet polynomials. But a classical non-trivial fact fue to Bohnenblust and Hille shows that if X is one dimensional, this maximal width heavily depends on the degree m of the Dirichlet polynomials. We carefully analyze this phenomenon, in particular in the setting of l(p)-spaces.