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Zh. Mat. Fiz. Anal. Geom., 2013, Volume 9, Number 4, Pages 582–593 (Mi jmag580)  

On the Skitovich–Darmois Theorem for $\mathbf{a}$-Adic Solenoids

I. P. Mazur

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv 61103, Ukraine

Abstract: By the Skitovich–Darmois theorem, the Gaussian distribution on the real line is characterized by the independence of two linear forms of $n$ independent random variables. The theorem is known to fail for a compact connected Abelian group even in the case when $n=2$. In the paper, it is proved that a weak analogue of the Skitovich–Darmois theorem holds for some $\mathbf{a}$-adic solenoids if we consider three independent linear forms of three random variables.

Key words and phrases: Skitovich–Darmois theorem, functional equation, $\mathbf{a}$-adic solenoid.

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Bibliographic databases:
MSC: 39B52, 62E10, 60B15
Received: 10.07.2013
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Citation: I. P. Mazur, “On the Skitovich–Darmois Theorem for $\mathbf{a}$-Adic Solenoids”, Zh. Mat. Fiz. Anal. Geom., 9:4 (2013), 582–593

Citation in format AMSBIB
\Bibitem{Maz13}
\by I.~P.~Mazur
\paper On the Skitovich--Darmois Theorem for $\mathbf{a}$-Adic Solenoids
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2013
\vol 9
\issue 4
\pages 582--593
\mathnet{http://mi.mathnet.ru/jmag580}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3155025}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000325604900007}


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