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On the Properties of an Entire Function of Two Complex Variables

Published online by Cambridge University Press:  20 November 2018

Arun Kumar Agarwal
Arun Kumar Agarwal*
Affiliation:
Department of Mathematics and Astronomy, Lucknow University, Lucknow, India
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1. Let

be an entire function of two complex variables z 1 and z 2, holomorphic in the closed polydisk . Let

Following S. K. Bose (1, pp. 214-215), μ(r 1, r 2; ƒ ) denotes the maximum term in the double series (1.1) for given values of r 1 and r 2 and v 1{m2; r 1, r 2) or v 1(r 1, r 2), r 2 fixed, v 2(m 1, r 1, r 2) or v 2(r 1, r 2), r 1 fixed and v(r 1r 2) denote the ranks of the maximum term of the double series (1.1).

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 51 - 57
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

This research has been supported by a Junior Research Fellowship, an award of the Council of Scientific and Industrial Research, New Delhi, India. The author is grateful to the referee for his helpful suggestions.

References

1. Bose, S. K. and Sharma, Devendra, Integral functions of two complex variables, Compositio Math., 15 (1963), 210–226.Google Scholar
2. Dikshit, G. P. and Agarwal, A. K., On the means of entire functions of several complex variables submitted for publication).Google Scholar
3. Fuks, B. A., Theory of analytic functions of several complex variables, (Moscow, 1963).10.1090/mmono/008CrossRefGoogle Scholar