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Stable \(\delta -\)Subharmonic Functions on the Nonlinear Homogeneous Spaces

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Abstract

We study stable \(\delta -\)subharmonic functions on the nonlinear homogeneous spaces ; here is a punctured Euclidean space \({{\mathbb {R}}^{3}}\backslash \{0\}\) and \(\mathcal {G}\) denotes a group of the compositions of elements from SO(3) with homotheties. A necessary and sufficient condition for a measure on to be the Riesz measure of a stable \(\delta -\)subharmonic function in is established. We also provide a representation for such functions.

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Acknowledgements

The author cordially thanks his supervisor Professor Andriy Kondratyuk, which passed away on April 22, 2016. Many thanks to Prof. Kondratyuk for the idea of this investigation and the useful remarks.

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  1. Ivan Franko National University of Lviv, Lviv, Ukraine

    Vasylyna Khoroshchak

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  1. Vasylyna Khoroshchak
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Correspondence to Vasylyna Khoroshchak.

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Communicated by Anatoly Golberg.

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Khoroshchak, V. Stable \(\delta -\)Subharmonic Functions on the Nonlinear Homogeneous Spaces. Complex Anal. Oper. Theory 11, 1587–1595 (2017). https://doi.org/10.1007/s11785-017-0639-7

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