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Treffer: criteria for sub harmonicity and continuation of sub harmonic functions: Criteria for (sub-)harmonicity and continuation of (sub-)harmonic functions

Title:
criteria for sub harmonicity and continuation of sub harmonic functions: Criteria for (sub-)harmonicity and continuation of (sub-)harmonic functions
Authors:
Bulat N. Khabibullin
Source:
Siberian Mathematical Journal. 44(4):713-728
Publisher Information:
Russian Academy of Sciences - RAS (Rossiĭskaya Akademiya Nauk - RAN), Siberian Branch (Sibirskoe Otdelenie), Sobolev Insitute of Mathematics (Institut Matematiki Im. S. L. Soboleva), Novosibirsk, 2003.
Publication Year:
2003
Subject Terms:
harmonic function, Entire functions of one complex variable (general theory), Jensen measure, Special classes of entire functions of one complex variable and growth estimates, Arens-Singer measure, subharmonic function, Harmonic, subharmonic, superharmonic functions in higher dimensions
Document Type:
Fachzeitschrift Article
File Description:
application/xml
ISSN:
0037-4466
DOI:
10.1023/a:1024796809786
Access URL:
https://zbmath.org/2007845
https://link.springer.com/article/10.1023%2FA%3A1024796809786
https://link.springer.com/content/pdf/10.1023/A:1024796809786.pdf
Accession Number:
edsair.dedup.wf.002..fdb7d20bf4d13367d865bb3fddd0b636
Database:
OpenAIRE

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Summary: We obtain criteria for harmonicity and subharmonicity of a function in a domain in \(\mathbb R^d\), \(d\geq 2\), in terms of special Arens-Singer and Jensen measures. We also establish a criterion for (sub-)harmonicity of a \(\delta\)-subharmonic function in terms of the associated Riesz charge and special Arens-Singer and Jensen functions. To this end, we use the theorem of this article on continuation of (sub-)harmonic functions to polar sets.