Our main results are certain developments of the classical Poisson -Jensen formula for subharmonic functions. The basis of the classical Poisson -Jensen formula is the natural duality between harmonic measures and Green's functions. Our generalizations use some duality between the balayage of measures and and their potentials.
Our main results are certain developments of the classical Poisson -Jensen formula for subharmonic functions. The basis of the classical Poisson -Jensen formula is the natural duality between harmonic measures and Green's functions. Our generalizations use some duality between the balayage of measures and and their potentials.
“…We have considered in the survey [46] general concepts of affine balayage. In this article we deal with a particular case of such balayage with respect to special classes of test subharmonic functions.…”
Section: Introductionmentioning
confidence: 99%
“…[46]). Let O ⊂ R d be an open subset, and S o D. Let V be a class of Borel-measurable functions on O \ S o .…”
“…We have are considered in the survey [14] various general concepts of balayage. In this article we deal with a particular case of such balayage with respect to special classes of test subharmonic functions.…”
We investigate some properties of balayage of charges and measures for subclasses of subharmonic functions and their relationship to the geometry of domain or open set in finite-dimensional Euclidean space where this balayage is considered.
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