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 Ufimsk. Mat. Zh., 2011, Volume 3, Issue 4, Pages 3–7 (Mi ufa111)

Theorem on commutation in the principal part

M. S. Akbasheva, A. B. Shabat

Karachay-Cherkess State University, Karachaevsk, Russia

Abstract: In the present paper we demonstrate how one can use the Poisson bracket in order to build up and to classify commuting pairs of partial differential operators with two independent variables. The commutativity condition is reduced to the simple functional equation with shifts of the arguments for considered operators. The Poisson bracket represents the limiting case of that functional equation in which the shifts are replaced by the corresponding directional derivatives.

Keywords: differential operators, commutators and the Poisson bracket, functional equation.

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Bibliographic databases:
UDC: 517.985

Citation: M. S. Akbasheva, A. B. Shabat, “Theorem on commutation in the principal part”, Ufimsk. Mat. Zh., 3:4 (2011), 3–7

Citation in format AMSBIB
\Bibitem{AkbSha11} \by M.~S.~Akbasheva, A.~B.~Shabat \paper Theorem on commutation in the principal part \jour Ufimsk. Mat. Zh. \yr 2011 \vol 3 \issue 4 \pages 3--7 \mathnet{http://mi.mathnet.ru/ufa111} \zmath{https://zbmath.org/?q=an:1249.47029}