Mathematica Bohemica, online first, 9 pp.


A study of various results for a class of entire Dirichlet series with complex frequencies

Niraj Kumar, Garima Manocha

Received July 16, 2016.  First published May 11, 2017.

Abstract:  Let $F$ be a class of entire functions represented by Dirichlet series with complex frequencies $\sum a_k {\rm e}^{\langle\lambda^k, z\rangle}$ for which $(|\lambda^k|/{\rm e})^{|\lambda^k|} k!|a_k|$ is bounded. Then $F$ is proved to be a commutative Banach algebra with identity and it fails to become a division algebra. $F$ is also proved to be a total set. Conditions for the existence of inverse, topological zero divisor and continuous linear functional for any element belonging to $F$ have also been established.
Keywords:  Dirichlet series; Banach algebra; topological zero divisor; division algebra; continuous linear functional; total set
Classification MSC:  30B50, 46J15, 17A35
DOI:  10.21136/MB.2017.0066-16

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References:
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Affiliations:   Niraj Kumar, Garima Manocha, Department of Mathematics, Netaji Subhas Institute of Technology, Azad Hind Fauz Marg, Sector 3, Dwarka, New Delhi-110078, India, e-mail: nirajkumar2001@hotmail.com, garima89.manocha@gmail.com

 
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