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How fast can a subharmonic function decayalong a ray?

Published online by Cambridge University Press:  01 January 1998

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Abstract

Much is knownabout the connection between the growth and decay of subharmonic functions. Theresults indicate that there is a general principle: {\em asubharmonic functioncannot decay ‘too fast’ relative to its growth}.Three theorems areproved which, together with work previously published elsewhere, give a fairlycomplete account of howthis principle works out for a subharmonic functionhaving extremal decay along a ray.

1991 Mathematics SubjectClassification: 30D20, 31A05.

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Type
Research Article
Copyright
London Mathematical Society 1998

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