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Transactions of the American Mathematical Society

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On the geometric means of entire functions of several complex variables


Author: A. K. Agarwal
Journal: Trans. Amer. Math. Soc. 151 (1970), 651-657
MSC: Primary 32.05
DOI: https://doi.org/10.1090/S0002-9947-1970-0264107-X
MathSciNet review: 0264107
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Abstract: Let $ f({z_1}, \ldots ,{z_n})$ be an entire function of the $ n( \geqq 2)$ complex variables $ {z_1}, \ldots ,{z_n}$, holomorphic for $ \vert{z_t}\vert \leqq {r_t},t = 1, \ldots ,n$. We have considered the case of only two complex variables for simplicity. Recently many authors have defined the arithmetic means of the function $ \vert f({z_1},{z_2})\vert$ and have investigated their properties. In the present paper, the geometric means of the function $ \vert f({z_1},{z_2})\vert$ have been defined and the asymptotic behavior of certain growth indicators for entire functions of several complex variables have been studied and the results are given in the form of theorems.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0264107-X
Keywords: Entire function, holomorphic, geometric means, order, lower order, Poisson formula in two variables, slowly changing function, regular growth
Article copyright: © Copyright 1970 American Mathematical Society

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