A study on bornological properties of the space of entire functions of several complex variables

Authors

  • Mushtaq Shaker Abdul-Hussein
  • G. S. Srivastava

DOI:

https://doi.org/10.5556/j.tkjm.33.2002.277

Abstract

Spaces of entire functions of several complex variables occupy an important position in view of their vast applications in various branches of mathematics, for instance, the classical analysis, theory of approximation, theory of topological bases etc. With an idea of correlating entire functions with certain aspects in the theory of basis in locally convex spaces, we have investigated in this paper the bornological aspects of the space $X$ of integral functions of several complex variables. By $Y$ we denote the space of all power series with positive radius of convergence at the origin. We introduce bornologies on $X$ and $Y$ and prove that $Y$ is a convex bornological vector space which is the completion of the convex bornological vector space $X$.

Author Biography

Mushtaq Shaker Abdul-Hussein

Department of Mathematics, University of Roorkee, Roorkee 247667, (U.P.), India.

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Published

2002-12-31

How to Cite

Abdul-Hussein, M. S., & Srivastava, G. S. (2002). A study on bornological properties of the space of entire functions of several complex variables. Tamkang Journal of Mathematics, 33(4), 289-302. https://doi.org/10.5556/j.tkjm.33.2002.277

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Section

Papers