Open AccessOn a characterization theorem on a-adic solenoids
Author(s) -
G. M. Feldman
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524893227-231
Subject(s) - solenoid , mathematics , distribution (mathematics) , real line , automorphism , random variable , gaussian , order (exchange) , pure mathematics , symmetry (geometry) , mathematical analysis , physics , quantum mechanics , geometry , statistics , finance , economics
According to the Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given the other. We prove an analogue of this theorem for linear forms of two independent random variables taking values in an -adic solenoid containing no elements of order 2. Coefficients of the linear forms are topological automorphisms of the -adic solenoid.