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Título:
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Bohr's strip for vector valued Dirichlet series
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Autores:
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Defant, Andreas ;
García, Domingo ;
Maestre, Manuel ;
Pérez García, David
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Tipo de documento:
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texto impreso
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Editorial:
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Springer, 2008
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/restrictedAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Análisis funcional y teoría de operadores
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Tipo = Artículo
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Resumen:
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Bohr showed that the width of the strip (in the complex plane) on which a given Dirichlet series Sigma a(n)/n(s), s is an element of C, converges uniformly but not absolutely, is at most 1/2, and Bohnenblust-Hille that this bound in general is optimal. We prove that for a given infinite dimensional Banach space Y the width of Bohr's strip for a Dirichlet series with coefficients a(n) in Y is bounded by 1 - 1/Cot (Y), where Cot (Y) denotes the optimal cotype of Y. This estimate even turns out to be optimal, and hence leads to a new characterization of cotype in terms of vector valued Dirichlet series.
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En línea:
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https://eprints.ucm.es/id/eprint/17787/1/PerezGarcia22.pdf
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