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How fast can a subharmonic function decayalong a ray?

Published online by Cambridge University Press:  01 January 1998

AM Ulanovskii
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Abstract

Much is known about the connection between the growth and decay of subharmonic functions. The results indicate that there is a general principle: {\em asubharmonic function cannot decay ‘too fast’ relative to its growth}.Three theorems are proved which, together with work previously published elsewhere, give a fairly complete account of how this principle works out for a subharmonic function having extremal decay along a ray.

1991 Mathematics Subject Classification: 30D20, 31A05.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 76 , Issue 1 , January 1998 , pp. 175 - 202
Copyright
London Mathematical Society 1998

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