A study of various results for a class of entire Dirichlet series with complex frequencies
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 beco...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2018-04-01
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| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/143/1/mb143_1_1.pdf |
| Summary: | 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. |
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| ISSN: | 0862-7959 2464-7136 |