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Subharmonicity of higher dimensional exponential transforms
Department of Mathematics, Volgograd State University, Russia.ORCID iD: 0000-0002-8422-6140
2005 (English)In: Quadrature domains and their applications: The Harold S. Shapiro Anniversary Volume / [ed] Peter Ebenfelt, Björn Gustafsson, Dmitry Khavinson, Mihai Putinar, Basel: Birkhäuser Verlag, 2005, Vol. 156, 257-277 p.Chapter in book (Refereed)
Abstract [en]

Our main result states that the function (1 − Eρis subharmonic, where 0 ≤ ρ ≤ 1 is a density function in ℝn, n ≥ 3, and E p (x)=exp(−2 n −− ∫ρ(ζ)dζ ∣ ∣ ζ−x∣ ∣ n ) , is the exponential transform of ρ. This answers in affirmative the recent question posed by B. Gustafsson and M. Putinar in [6].

Place, publisher, year, edition, pages
Basel: Birkhäuser Verlag, 2005. Vol. 156, 257-277 p.
, Operator Theory: advances and applications, 156
Keyword [en]
Exponential transform; subharmonic functions; moments; Riesz potential
National Category
Mathematical Analysis
URN: urn:nbn:se:liu:diva-89272DOI: 10.1007/3-7643-7316-4_13ISBN: 978-3-7643-7145-6OAI: diva2:607596
Available from: 2013-02-25 Created: 2013-02-25 Last updated: 2014-10-08

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Tkachev, Vladimir
Mathematical Analysis

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