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The Phragemén‐Lindelöf principle of harmonic functions and conditions for nevanlinna class in the half space
Author(s) -
Zhang Yan Hui
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5655
Subject(s) - mathematics , subharmonic function , class (philosophy) , subharmonic , hilbert space , representation (politics) , space (punctuation) , harmonic function , pure mathematics , harmonic , mathematical analysis , analytic function , nonlinear system , law , linguistics , philosophy , physics , quantum mechanics , artificial intelligence , politics , computer science , political science
In this article, we firstly discuss a kind of Phragemén‐Lindelöf Principle of harmonic functions by using the Nevanlinna's representation in the high dimensional space. Secondly, we derive the sufficient conditions for subharmonic functions being in the Nevanlinna class as well. These results are main tools to study the Hilbert space of harmonic functions with analytic approaches and generalizations of some classic results.