On a class of vector-valued entire Dirichlet series in n variables

Lakshika Chutani; Niraj Kumar; Garima Manocha

doi:10.12697/ACUTM.2018.22.01

Lakshika Chutani Department of Mathematics, Netaji Subhas Institute of Technology, Sec- tor 3 Dwarka, New Delhi-110078
Niraj Kumar Department of Mathematics, Netaji Subhas Institute of Technology, Sec- tor 3 Dwarka, New Delhi-110078
Garima Manocha Department of Mathematics, Bhagwan Parshuram Institute of Technology, PSP-4, Dr KN Katju Marg, Sector 17 Rohini, New Delhi-110089

DOI: https://doi.org/10.12697/ACUTM.2018.22.01

Keywords: Dirichlet series, Banach algebra, quasi-inverse, spectrum, total set

Abstract

We consider a class F of entire Dirichlet series in n variables, whose coefficients belong to a commutative Banach algebra E. With a well defined norm, F is proved to be a Banach algebra with identity. Further results on quasi-invertibility, spectrum and continuous linear functionals are proved for elements belonging to F.

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