Geodesic
A study of various results for a class of entire Dirichlet series with complex frequencies
Mathematica Bohemica, Tome 143 (2018) no. 1, pp. 1-9
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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.
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.
DOI : 10.21136/MB.2017.0066-16
Classification : 17A35, 30B50, 46J15
Keywords: Dirichlet series; Banach algebra; topological zero divisor; division algebra; continuous linear functional; total set 
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Kumar, Niraj; Manocha, Garima. A study of various results for a class of entire Dirichlet series with complex frequencies. Mathematica Bohemica, Tome 143 (2018) no. 1, pp. 1-9. doi: 10.21136/MB.2017.0066-16

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