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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On the geometric means of entire functions of several complex variables
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by A. K. Agarwal PDF
Trans. Amer. Math. Soc. 151 (1970), 651-657 Request permission

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 $|{z_t}| \leqq {r_t},t = 1, \ldots ,n$. We have considered the case of only two complex variables for simplicity. Recently many authors have defined the arithmetic means of the function $|f({z_1},{z_2})|$ and have investigated their properties. In the present paper, the geometric means of the function $|f({z_1},{z_2})|$ 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
  • Salomon Bochner and William Ted Martin, Several Complex Variables, Princeton Mathematical Series, vol. 10, Princeton University Press, Princeton, N. J., 1948. MR 0027863
  • S. K. Bose and Devendra Sharma, Integral functions of two complex variables, Compositio Math. 15 (1963), 210–226 (1963). MR 162966
  • G. H. Hardy and W. W. Rogosinski, Notes on Fourier series. III. Asymptotic formulae for the sums of certain trigonometrical series, Quart. J. Math. Oxford Ser. 16 (1945), 49–58. MR 14159, DOI 10.1093/qmath/os-16.1.49
  • R. K. Srivastava, Integral functions represented by Dirichlet series and integral functions of several complex variables, Ph.D. Thesis, Lucknow Univ., Lucknow, India, 1964.
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • 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