The decay of subharmonic functions of finite order along a ray
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- by J. M. Anderson and A. M. Ulanovsky PDF
- Proc. Amer. Math. Soc. 123 (1995), 3725-3730 Request permission
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 \[ B(r) = \sup \{ u(z):|z| < r\} .\] 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
- Arne Beurling, Some theorems on boundedness of analytic functions, Duke Math. J. 16 (1949), 355–359. MR 29980
- W. K. Hayman, Subharmonic functions. Vol. 2, London Mathematical Society Monographs, vol. 20, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1989. MR 1049148 —, The minimum modulus of integral functions of order one, J. Analyse Math. 28 (1975), 171-212. A. M. Ulanovsky, How fast can a subharmonic function decay along a ray? (to appear).
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3725-3730
- MSC: Primary 31A05; Secondary 30D15
- DOI: https://doi.org/10.1090/S0002-9939-1995-1277089-1
- MathSciNet review: 1277089