| Title:
|
A study of various results for a class of entire Dirichlet series with complex frequencies (English) |
| Author:
|
Kumar, Niraj |
| Author:
|
Manocha, Garima |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
143 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
1-9 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Dirichlet series |
| Keyword:
|
Banach algebra |
| Keyword:
|
topological zero divisor |
| Keyword:
|
division algebra |
| Keyword:
|
continuous linear functional |
| Keyword:
|
total set |
| MSC:
|
17A35 |
| MSC:
|
30B50 |
| MSC:
|
46J15 |
| idZBL:
|
Zbl 06861588 |
| idMR:
|
MR3778046 |
| DOI:
|
10.21136/MB.2017.0066-16 |
| . |
| Date available:
|
2018-03-19T10:32:28Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147136 |
| . |
| Reference:
|
[1] Khoi, L. H.: Coefficient multipliers for some classes of Dirichlet series in several complex variables.Acta Math. Vietnam. 24 (1999), 169-182. Zbl 0942.32001, MR 1710776 |
| Reference:
|
[2] Kumar, N., Manocha, G.: A class of entire Dirichlet series as an FK-space and a Fréchet space.Acta Math. Sci., Ser. B, Engl. Ed. 33 (2013), 1571-1578. Zbl 1313.30007, MR 3116603, 10.1016/S0252-9602(13)60105-8 |
| Reference:
|
[3] Kumar, N., Manocha, G.: On a class of entire functions represented by Dirichlet series.J. Egypt. Math. Soc. 21 (2013), 21-24. Zbl 1277.30004, MR 3040754, 10.1016/j.joems.2012.10.008 |
| Reference:
|
[4] Kumar, N., Manocha, G.: Certain results on a class of entire functions represented by Dirichlet series having complex frequencies.Acta Univ. M. Belii, Ser. Math. 23 (2015), 95-100. Zbl 1336.30004, MR 3373834 |
| Reference:
|
[5] Larsen, R.: Banach Algebras---An Introduction.Pure and Applied Mathematics 24. Marcel Dekker, New York (1973). Zbl 0264.46042, MR 0487369 |
| Reference:
|
[6] Larsen, R.: Functional analysis---An Introduction.Pure and Applied Mathematics 15. Marcel Dekker, New York (1973). Zbl 0261.46001, MR 0461069 |
| Reference:
|
[7] Srivastava, R. K.: Some growth properties of a class of entire Dirichlet series.Proc. Natl. Acad. Sci. India, Sect. A 61 (1991), 507-517. Zbl 0885.30004, MR 1169262 |
| Reference:
|
[8] Srivastava, R. K.: On a paper of Bhattacharya and Manna.Internal Report (1993), IC/93/417. |
| . |
