Email this article On a characterization theorem on a-adic solenoids
- Authors: Feldman G.M.1
-
Affiliations:
- B.Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine
- Issue: Vol 489, No 3 (2019)
- Pages: 227-231
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/18576
- DOI: https://doi.org/10.31857/S0869-56524893227-231
- ID: 18576
Cite item
Full Text
Abstract
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 α-adic solenoid containing no elements of order 2. Coefficients of the linear forms are topological automorphisms of the α-adic solenoid.
About the authors
G. M. Feldman
B.Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine
Author for correspondence.
Email: feldman@ilt.kharkov.ua
Ukraine, 47, Lenin prospect, Kharkov, 61103
References
- Heyde C.C. // Sankhya. Ser. A. 1970. V. 32. P. 115-118.
- Каган А.М., Линник Ю.В., Рао С.Р. Характеризационные задачи математической статистики. М.: Наука, 1972. 656 с.
- Feldman G.M. // J. Theoretical Probab. 2004. V. 17. P. 929-941.
- Миронюк М.В., Фельдман Г.М. // Сиб. мат. журнал. 2005. Т. 46. С. 403-415.
- Feldman G.M. // Probab. Theory Relat. Fields. 2005. V. 133. P. 345-357.
- Feldman G.M. // Studia Math. 2006. V. 177. P. 67-79.
- Feldman G.M. // J. Funct. Anal. 2010. V. 258. P. 3977-3987.
- Feldman G.M. // Math. Nachr. 2013. V. 286. P. 340-348.
- Myronyuk M.V. // Colloquium Mathematicum. 2013. V. 132. P. 195-210.
- Feldman G.M. // Publicationes Mathematicae Debrecen. 2015. V. 87. P. 147-166.
- Фельдман Г.М. // Теор. вероятн. и ее применения. 2017. Т. 62. С. 499-517.
- Feldman G.M. Functional Equations and Characterization Problems on Locally Compact Abelian Groups. EMS Tracts in Mathematics. Zurich: Europ. Math. Soc., 2008. V. 5. 268 p.
- Parthasarathy K.R. Probability Measures on Metric Spaces. N.Y.; L.: Acad. Press, 1967. 276 p.
- Хьюитт Э., Росс К. Абстрактный гармонический анализ. 1975. Т. 1. М.: Наука, 1975. 656 с.
- Feldman G.M. // Probab. Theory Relat. Fields. 2003. V. 126. P. 91-102.
Supplementary files
