Biblioteca de la Universidad Complutense de Madrid

Bohr's strip for vector valued Dirichlet series

Impacto

Defant, Andreas y García, Domingo y Maestre, Manuel y 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 Sólo personal autorizado del repositorio hasta 2020.

268kB

URL Oficial: http://www.springerlink.com/content/a3k0122058uw8228/fulltext.pdf




Resumen

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.


Tipo de documento:Artículo
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:17787
Referencias:

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)

Depositado:21 Ene 2013 11:28
Última Modificación:03 Dic 2014 09:06

Sólo personal del repositorio: página de control del artículo