Uniqueness theorems for subharmonic functions
B. N. Khabibullin
TL;DR
This paper proves that if two subharmonic functions agree outside a certain set, then they are identical everywhere, highlighting a uniqueness property for subharmonic functions.
Contribution
It establishes new uniqueness theorems for subharmonic functions based on their agreement outside specific sets.
Findings
Subharmonic functions coincide everywhere if they agree outside certain sets.
Theorems extend previous uniqueness results for harmonic functions.
Results have implications for potential theory and complex analysis.
Abstract
It is shown that harmonic functions on some subsets, subharmonic and coinciding everywhere outside of these sets, actually coincide everywhere.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Mathematical Modeling in Engineering · Spectral Theory in Mathematical Physics