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How Fast can a Subharmonic Function Decay Along a Ray?
Author(s) -
Ulanovskii AM
Publication year - 1998
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611598000069
Subject(s) - subharmonic , mathematics , function (biology) , connection (principal bundle) , work (physics) , subharmonic function , mathematical analysis , pure mathematics , physics , geometry , quantum mechanics , nonlinear system , evolutionary biology , biology
Much is known about the connection between the growth and decay of subharmonic functions. The results indicate that there is a general principle: 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.