Acta mathematica scientia, Series B >
A CLASS OF ENTIRE DIRICHLET SERIES AS AN FK-SPACE AND A FRECHET SPACE
Received date: 2012-06-12
Revised date: 2013-04-07
Online published: 2013-11-20
In the present paper we consider a class of entire functions represented by Dirichlet series whose coefficients belong to a commutative Banach algebra and prove it to be a complex FK-space and a Frechet space.
Key words: Dirichlet series; Banach algebra; FK-space; Frechet space
Niraj KUMAR , Garima MANOCHA . A CLASS OF ENTIRE DIRICHLET SERIES AS AN FK-SPACE AND A FRECHET SPACE[J]. Acta mathematica scientia, Series B, 2013 , 33(6) : 1571 -1578 . DOI: 10.1016/S0252-9602(13)60105-8
[1] Srivastava G S, Sharma A. Bases in the space of vector valued analytic Dirichlet series. Int J Pure Appl Math, 2011, 70: 993–1000
[2] Srivastava G S, Sharma A. Spaces of entire functions represented by vector valued Dirichlet series. J Math Appl, 2011, 34: 97–107
[3] Kamthan P K. FK-space for entire Dirichlet functions. Collect Math, 1969, 20: 271–280
[4] Srivastava R K. On the space of integral functions represented by Dirichlet series. Prog Maths, 1987, 21(1): 29–40
[5] Srivastava R K. On a paper of Bhattacharya and Manna. Internal Report, IC/93/417, 1993
[6] Larsen R. Banach Algebras: An Introduction. New York: Marcel Dekker Inc, 1973
[7] Larsen R. Functional Analysis: An Introduction. New York: Marcel Dekker Inc, 1973
[8] Srivastava B L. A Study of Spaces of Certain Classes of Vector Valued Dirichlet Series[D]. I I T Kanpur, 1983
[9] Kong Y, Gan H. On orders and types of Dirichlet series of slow growth. Turk J Math, 2010, 34: 1–11
[10] Kong Y Y. On some q-orders and q-types of Dirichlet-Hadamard product function. Acta Mathematica Sinica, Chinese Series, 2009, 52: 1165–1172
[11] Yu J R. Dirichlet Series and Random Dirichlet Series. Beijing: Science Press, 1997
/
| 〈 |
|
〉 |