Abstract:
A measure μ defined on the complex sphere S is called pluriharmonic if its Poisson integral is a pluriharmonic function (in the unit ball of Cn). А probability measure ρ is called representing if ∫Sfdρ=f(0) for all f in the ball algebra. It is shown that singular parts of pluriharmonic measures and representing measures are mutually singular. Bibliography: 5 titles.
Citation:
E. S. Dubtsov, “Singular parts of pluriharmonic measures”, Investigations on linear operators and function theory. Part 22, Zap. Nauchn. Sem. POMI, 217, POMI, St. Petersburg, 1994, 54–58; J. Math. Sci. (New York), 85:2 (1997), 1790–1793
\Bibitem{Dub94}
\by E.~S.~Dubtsov
\paper Singular parts of pluriharmonic measures
\inbook Investigations on linear operators and function theory. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 1994
\vol 217
\pages 54--58
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5959}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1327514}
\zmath{https://zbmath.org/?q=an:0869.31009|0907.31007}
\transl
\jour J. Math. Sci. (New York)
\yr 1997
\vol 85
\issue 2
\pages 1790--1793
\crossref{https://doi.org/10.1007/BF02355288}
Linking options:
https://www.mathnet.ru/eng/znsl5959
https://www.mathnet.ru/eng/znsl/v217/p54
This publication is cited in the following 4 articles:
Aleksei B. Aleksandrov, Evgueni Doubtsov, “Clark measures and de Branges–Rovnyak spaces in several variables”, Complex Variables and Elliptic Equations, 68:2 (2023), 212
Aleksei B. Aleksandrov, Evgueni Doubtsov, Trends in Mathematics, 12, Extended Abstracts Fall 2019, 2021, 9
Aleksandrov A.B., Doubtsov E., “Clark Measures on the Complex Sphere”, J. Funct. Anal., 278:2 (2020), UNSP 108314
Aleksandrov A.B., Doubtsov E., “Pluriharmonic Clark Measures and Analogs of Model Spaces”, C. R. Math., 357:1 (2019), 7–12
Citation in format AMSBIB
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