Abstract
Our main result states that the function (1 − E ρ is subharmonic, where 0 ≤ ρ ≤ 1 is a density function in ℝn, n ≥ 3, and \(E_p \left( x \right) = \exp \left( { - \tfrac{2} {n}\rlap{--} \smallint \tfrac{{\rho \left( \zeta \right)d\zeta }} {{\left| {\zeta - x} \right|^n }}} \right)\), is the exponential transform of ρ. This answers in affirmative the recent question posed by B. Gustafsson and M. Putinar in [6].
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© 2005 Birkhäuser Verlag Basel/Switzerland
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Tkachev, V.G. (2005). Subharmonicity of Higher Dimensional Exponential Transforms. In: Ebenfelt, P., Gustafsson, B., Khavinson, D., Putinar, M. (eds) Quadrature Domains and Their Applications. Operator Theory: Advances and Applications, vol 156. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7316-4_13
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