Complutense University Library

Bohr's strip for vector valued Dirichlet series

Defant, Andreas and García, Domingo and Maestre, Manuel and Pérez García, David (2008) Bohr's strip for vector valued Dirichlet series. Mathematische Annalen, 342 (3). pp. 533-555. ISSN 0025-5831

[img] PDF
Restringido a Repository staff only hasta 2020.


Official URL:

View download statistics for this eprint

==>>> Export to other formats


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.

Item Type:Article
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:17787

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)

Deposited On:21 Jan 2013 11:28
Last Modified:03 Dec 2014 09:06

Repository Staff Only: item control page