Spaces of vector-valued Dirichlet series in a half plane

Abstract

Dirichlet series with real frequencies which represent entire functions on the complex plane ℂ have been investigated by many authors. Several proeperties such as topological structures, linear continuous functionals, and bases have been considered. Le Hai Khoi drived some results with Dirichlet series having negative real frequencies which represent holomorphic functions in a half plane. In the present paper, we have obtained some properties of holomorphic Dirichlet series having positive exponents, whose coefficients belong to a Banach algebra.

Keywords

Vector-valued Dirichlet series / abscissa of convergence / norm / topology

References

[1] Huo Y Y, Kong Y Y. On generalized order and generalized type of Dirichlet series in the right half plane. Acta Math Sci Ser B Engl Ed, 2014, 34(1): 175-182

[2] Khoi L H. Holomorphic Dirichlet series in the half plane. Vietnam J Math, 1998, 26: 259-271

[3] Kong Y Y, Gan H L. On orders and types of Dirichlet series of slow growth. Turkish J Math, 2010, 34: 1-11

[4] Kong Y Y, Hong Y. On the Growth of Laplace-Stieltjes Transforms and the Singular Direction of Complex Analysis. Guangzhou: Jinan University Press, 2010

[5] Srivastava B L. A Study of Spaces of Certain Classes of Vector Valued Dirichlet Series. Thesis. I I T Kanpur, 1983

[6] Srivastava G S, Sharma A. Bases in the space of vector valued analytic Dirichlet series. Int J Pure Appl Math, 2011, 70(7): 993-1000<?Pub Caret?>

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg