Convergence of Dirichlet polynomials in Banach spaces
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- by Andreas Defant and Pablo Sevilla-Peris PDF
- Trans. Amer. Math. Soc. 363 (2011), 681-697 Request permission
Abstract:
Recent results on Dirichlet series $\sum _{n} a_{n} \frac {1}{n^{s}}$, $s \in \mathbb {C}$, 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 due 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 $\ell _p$-spaces.References
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Additional Information
- Andreas Defant
- Affiliation: Institute of Mathematics, Carl von Ossietzky University, D–26111 Oldenburg, Germany
- Email: defant@mathematik.uni-oldenburg.de
- Pablo Sevilla-Peris
- Affiliation: Institute of Mathematics, Carl von Ossietzky University, D–26111 Oldenburg, Germany – and – Departamento de Matemática Aplicada and IUMPA, ETSMRE, Universidad Politécnica de Valencia, Av. Blasco Ibáñez, 21, E–46010 Valencia, Spain
- MR Author ID: 697317
- ORCID: 0000-0001-5222-4768
- Email: psevilla@mat.upv.es
- Received by editor(s): July 14, 2008
- Received by editor(s) in revised form: March 7, 2009
- Published electronically: September 15, 2010
- Additional Notes: Both authors were supported by the MEC Project MTM2008-03211. The second author was partially supported by grants PR2007-0384 (MEC) and UPV-PAID-00-07.
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 681-697
- MSC (2000): Primary 46B07; Secondary 32A05, 46B09, 46G20, 30B50
- DOI: https://doi.org/10.1090/S0002-9947-2010-05146-3
- MathSciNet review: 2728583