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

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg