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The decay of subharmonic functions of finite order along a ray

Authors: J. M. Anderson and A. M. Ulanovsky
Journal: Proc. Amer. Math. Soc. 123 (1995), 3725-3730
MSC: Primary 31A05; Secondary 30D15
MathSciNet review: 1277089
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Abstract: A result is proved relating the growth of a subharmonic function $ u(z)$ of finite lower order at least one, along a ray, to the quantity

$\displaystyle B(r) = \sup \{ u(z):\vert z\vert < r\} .$

This sharpens a previous result of the second author when the lower order is finite. An example is constructed to show that the result obtained is best possible.

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

  • [1] Arne Beurling, Some theorems on boundedness of analytic functions, Duke Math. J. 16 (1949), 355–359. MR 0029980
  • [2] W. K. Hayman, Subharmonic functions. Vol. 2, London Mathematical Society Monographs, vol. 20, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1989. MR 1049148
  • [3] -, The minimum modulus of integral functions of order one, J. Analyse Math. 28 (1975), 171-212.
  • [4] A. M. Ulanovsky, How fast can a subharmonic function decay along a ray? (to appear).

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Article copyright: © Copyright 1995 American Mathematical Society

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