Bohr's strip for vector valued Dirichlet series
| dc.contributor.author | Defant, Andreas | |
| dc.contributor.author | García, Domingo | |
| dc.contributor.author | Maestre, Manuel | |
| dc.contributor.author | Pérez García, David | |
| dc.date.accessioned | 2023-06-20T09:45:15Z | |
| dc.date.available | 2023-06-20T09:45:15Z | |
| dc.date.issued | 2008 | |
| dc.description.abstract | 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. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MEC and FEDER | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17787 | |
| dc.identifier.doi | 10.1007/s00208-008-0246-z | |
| dc.identifier.issn | 0025-5831 | |
| dc.identifier.officialurl | http://www.springerlink.com/content/a3k0122058uw8228/fulltext.pdf | |
| dc.identifier.relatedurl | http://www.springerlink.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50304 | |
| dc.issue.number | 3 | |
| dc.journal.title | Mathematische Annalen | |
| dc.language.iso | eng | |
| dc.page.final | 555 | |
| dc.page.initial | 533 | |
| dc.publisher | Springer | |
| dc.relation.projectID | MTM2005-08210 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Bohr's strip for vector valued Dirichlet series | |
| dc.type | journal article | |
| dc.volume.number | 342 | |
| dcterms.references | Boas, H.P.: The football player and the infinite series. Not. AMS 44, 1430–1435 (1997) Bombal, F., Pérez-García, D., Villanueva, I.: Multilinear extensions of Grothendieck’s theorem. Q. J. Math. 55, 441–450 (2004) Bohnenblust, H.F., Hille, E.: On the absolute convergence of Dirichlet series. Ann. Math. 32(2), 600–622 (1934) Bohr, H.: Über die gleichmässige Konverenz Dirichletscher Reihen. J. Reine Angew. Math. 143, 203–211 (1913) Bohr, H.: Über die Bedeutung der Potenzreihen unendlich vieler Variabeln in der Theorie der Dirichletschen Reihen anns . Nachr. Ges. Wiss. Gött. Math. Phys. Kl. 4, 441–488 (1913) Bohr, H.: A theorem concerning power series. Proc. Lond. Math. Soc. 13(2), 1–5 (1914) Defant, A., García, D., Maestre, M.: New strips of convergence for Dirichlet series. Preprint (2008) Defant, A., Maestre, M., Prengel, C.: Domains of convergence for monomial expansions of holomorphic functions in infinitely many variables. J. Reine Angew. Math. (2008) (to appear) Defant, A., Prengel, C.: Harald Bohr meets Stefan Banach. Lond. Math. Soc. Lect. Note Ser. 337, 317–339 (2006) Dineen, S.: Complex Analysis on Infinite Dimensional Spaces. Springer, London (1999) Diestel, J., Jarchow, H., Tonge, A.: Absolutely summing operators. Cambridge Stud. Adv. Math., vol. 43. Cambridge University Press, Cambridge (1995) Hedenmalm, H.: Dirichlet series and functional analysis, The legacy ofNiels Henrik Abel, pp. 673–684. Springer, Berlin (2004) Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces I. Springer, Berlin (1977) Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces II. Springer, Berlin (1979) Maurey, B., Pisier, G.: Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach. Stud. Math. 58, 45–90 (1976) Mujica, J.: Complex analysis in Banach spaces. Math. Studies, vol. 120. North Holland, Amsterdam (1986) Queffélec, H.: H. Bohr’s vision of ordinary Dirichlet series; old and newresults. J.Anal. 3, 43–60 (1995) Toeplitz, O.: Über eine bei Dirichletreihen auftretende Aufgabe aus der Theorie der Potenzreihen unendlich vieler Veraenderlichen. Nachr. Ges. Wiss. Gött. Math. Phys. Kl. 417–432 (1913) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 5edb2da8-669b-42d1-867d-8fe3144eb216 | |
| relation.isAuthorOfPublication.latestForDiscovery | 5edb2da8-669b-42d1-867d-8fe3144eb216 |
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