Carleman’s Formula for -Analytic Functions

In this paper, we investigate -analytic functions, where is a function that is antianalytic. The article demonstrates the existence of an -harmonic measure at most points on the boundary of a lemniscate. The main contribution of this paper is the development of a new quenching function for -analytic...

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Bibliographic Details
Published inLobachevskii journal of mathematics Vol. 45; no. 12; pp. 6659 - 6667
Main Authors Zhabborov, N. M., Narzillaev, N. Kh, Husenov, B. E.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2024
Springer Nature B.V
Subjects
Algebra
Analysis
Analytic functions
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Quenching
analytic functions
Hardy class
harmonic measures
2010 Mathematics Subject Classification: 30C62, 30B30, 31A25
lemniscate
boundary values
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Summary:In this paper, we investigate -analytic functions, where is a function that is antianalytic. The article demonstrates the existence of an -harmonic measure at most points on the boundary of a lemniscate. The main contribution of this paper is the development of a new quenching function for -analytic functions. This quenching function is used to derive Carleman formula for -analytic functions in the Hardy class.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224607823