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). A probability measure ρ is called representing if ∫Sfdp=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.
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References
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 217, 1994, pp. 54–58.
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Dubtsov, E.S. Singular parts of pluriharmonic measures. J Math Sci 85, 1790–1793 (1997). https://doi.org/10.1007/BF02355288
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DOI: https://doi.org/10.1007/BF02355288