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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A note on the geometric means of entire functions of several complex variables


Author: P. K. Kamthan
Journal: Trans. Amer. Math. Soc. 169 (1972), 503-508
MSC: Primary 32A15
MathSciNet review: 0508027
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Abstract: Let $ f({z_1}, \cdots ,{z_n})$ be an entire function of $ n( \geqslant 2)$ complex variables. Recently Agarwal [Trans. Amer. Math. Soc. 151 (1970), 651-657] has obtained certain results involving geometric mean values of $ f$. In this paper we have constructed examples to contradict some of the results of Agarwal and have thereafter given improvements and modifications of his results.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0508027-3
PII: S 0002-9947(1972)0508027-3
Keywords: Entire function, geometric means, order, Poisson formula for two variables, slowly changing function
Article copyright: © Copyright 1972 American Mathematical Society