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Bornological spaces of (entire functions represented by Dirichlet series having slow growth

Journal Name:

  • İstanbul Üniversitesi Fen Fakültesi Matematik, Fizik ve Astronomi Dergisi

Publication Year:

  • 2001
Author NameUniversity of Author
Abstract (2. Language): 
The study of spaces of entire functions was initiated by V.G. Iyer [6] and the space of entire functions represented by Dirichlet series has been studied by Hussein and Kamthan [4] and others. Patwardhan [9] has successfully studied bornological properties of the spaces of entire function in terms of the coefficients of Taylor series expansions. In this paper we have used another norm and study the bornological aspects of the space F of all 00 entire Dirichlet series a{s) ~ ^ an exp(sAn) of order zero.
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  • 60
19-32
  • English

REFERENCES

References: 

[1] Bernstein, V. - Lecons sur les progres recents de la theorie des series de Dirichlet. Gauthiers-Villars, Paris, (1933).
[2] Hogbe-Nlend, H. - The'oriedes Bomologies et Applications. Lecture Notes, Springer-verlag, Berlin, No. 213, (1971).
[3] Hogbe -Nlend, H. - Bomologies and functional analysis. North-Holland publishing company, Netherlands, (1977).
[4] Hussain, Taqdir and Kamthan, P.K, - Spaces of entire functions represented by Dirichlet series, Collectania Mathematica, 19 (3), (1968): 203-216.
31
Mushtaq Shaker and G.S. Srivastava
[5] Iyer, V.G. - A property of the maximum modulus of integral functions. J. Indian Math. Soc, 6 (1942): 69-80.
[6] Iyer, V.G. - On the space o:f integral functions (I). J. Indian Math. Soc. (New Series), 12, (1948): 13-30.
[7] Kamthan, P.K. and S.K, Singh Gautam - Bases in the space of analytic Dirichlet transformations. Collect. Math. 23, (1972): 9-16.
[8] Kamthan, P.K. and S.K. Singh Gautam - Bases in a certain space of Dirichlet entire transformations. Indian J. Pure Appl. Math. 6 (8), (1975): 856-863.
[9] Patwardhan, M.D. - Study on bomological properties'of the space of integral functions. Indian J. Pure Appl. Math. 12 (7), (1981): 865-873.
[10] Prem Singh - Some aspects of the growth of entire functions and Dirichlet series, Thesis. I..I.T. Kanpur, 1966.
[11] Ritt, J.F. - A note on the proximate order of entire functions represented by Dirichlet series, Bull, de L'Academie Polonaise des Sciences, 19 (3), (1971): 199-202,

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