On the volume of a spherical octahedron with symmetries |
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| Authors: | N. V. Abrosimov M. Godoy-Molina A. D. Mednykh |
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| Affiliation: | 1.Institut für Mathematik C,Technische Universit?t,Graz,Austria |
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| Abstract: | The group Aff(ℚ) of affine transformations with rational coefficients acts naturally not only on the real line ℝ, but also on the p-adic fields ℚp. The aim of this note is to show that all these actions are necessary and sufficient to represent bounded μ-harmonic functions for a probability measure μ on Aff(ℚ) that is supported by a finitely generated subgroup, that is, to describe the Poisson boundary. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 50, Functional Analysis, 2007. |
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