Coefficient multipliers on spaces of vector-valued entire Dirichlet series

Sharma Akanksha; Girja S. Srivastava

Mathematica Bohemica (2017)

  • Volume: 142, Issue: 3, page 299-307
  • ISSN: 0862-7959

Abstract

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The spaces of entire functions represented by Dirichlet series have been studied by Hussein and Kamthan and others. In the present paper we consider the space X of all entire functions defined by vector-valued Dirichlet series and study the properties of a sequence space which is defined using the type of an entire function represented by vector-valued Dirichlet series. The main result concerns with obtaining the nature of the dual space of this sequence space and coefficient multipliers for some classes of vector-valued Dirichlet series.

How to cite

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Akanksha, Sharma, and Srivastava, Girja S.. "Coefficient multipliers on spaces of vector-valued entire Dirichlet series." Mathematica Bohemica 142.3 (2017): 299-307. <http://eudml.org/doc/294103>.

@article{Akanksha2017,
abstract = {The spaces of entire functions represented by Dirichlet series have been studied by Hussein and Kamthan and others. In the present paper we consider the space $X$ of all entire functions defined by vector-valued Dirichlet series and study the properties of a sequence space which is defined using the type of an entire function represented by vector-valued Dirichlet series. The main result concerns with obtaining the nature of the dual space of this sequence space and coefficient multipliers for some classes of vector-valued Dirichlet series.},
author = {Akanksha, Sharma, Srivastava, Girja S.},
journal = {Mathematica Bohemica},
keywords = {vector-valued Dirichlet series; analytic function; entire function; dual space; norm},
language = {eng},
number = {3},
pages = {299-307},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Coefficient multipliers on spaces of vector-valued entire Dirichlet series},
url = {http://eudml.org/doc/294103},
volume = {142},
year = {2017},
}

TY - JOUR
AU - Akanksha, Sharma
AU - Srivastava, Girja S.
TI - Coefficient multipliers on spaces of vector-valued entire Dirichlet series
JO - Mathematica Bohemica
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 142
IS - 3
SP - 299
EP - 307
AB - The spaces of entire functions represented by Dirichlet series have been studied by Hussein and Kamthan and others. In the present paper we consider the space $X$ of all entire functions defined by vector-valued Dirichlet series and study the properties of a sequence space which is defined using the type of an entire function represented by vector-valued Dirichlet series. The main result concerns with obtaining the nature of the dual space of this sequence space and coefficient multipliers for some classes of vector-valued Dirichlet series.
LA - eng
KW - vector-valued Dirichlet series; analytic function; entire function; dual space; norm
UR - http://eudml.org/doc/294103
ER -

References

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  1. Khôi, L. H., Holomorphic Dirichlet series in the half plane, Vietnam J. Math. 26 (1998), 259-271. (1998) Zbl0935.30002MR1684343
  2. Mandelbrojt, S., Dirichlet series, Rice Inst. Pamphlet 31 159-272 (1944). (1944) Zbl0063.03767MR0012163
  3. Srivastava, B. L., A Study of Spaces of Certain Classes of Vector Valued Dirichlet Series, Thesis. Indian Institute of Technology Kanpur (1983). (1983) 

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