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Ufa Mathematical Journal, 2011, Volume 3, Issue 2, Pages 89–95 (Mi ufa97)  
This article is cited in 2 scientific papers (total in 2 papers)

Commuting differential operators in two-dimension

A. B. Shabat, Z. S. Elkanova

Aliev Karachaevo-Cherkesiya State University, Karachaevsk, Republic of Karachaevo-Cherkesiya, Russia
English version PDF (367 kB) Citations (2)
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Abstract: A generalization to the multi-dimensional case of commutative rings of differential operators is considered. An algorithm for construction of commuting two-dimensional differential operators is formulated for a special kind of operators related to the simple one-dimensional model proposed by Burchnall and Chaundy in 1932. The problem of classifying such commutative pairs is discussed. The suggested algorithm is based on necessary conditions for general commutativity and the reducibility lemma proved in the present paper.
Keywords: commuting ring of differential operators, commuting two-dimensional differential operators.
Received: 10.05.2011
Russian version:
Ufimskii Matematicheskii Zhurnal, 2011, Volume 3, Issue 2, Pages 91–98
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: English
Original paper language: Russian
Citation: A. B. Shabat, Z. S. Elkanova, “Commuting differential operators in two-dimension”, Ufimsk. Mat. Zh., 3:2 (2011), 91–98; Ufa Math. J., 3:2 (2011), 89–95
Citation in format AMSBIB
\Bibitem{ShaElk11}
\by A.~B.~Shabat, Z.~S.~Elkanova
\paper Commuting differential operators in two-dimension
\jour Ufimsk. Mat. Zh.
\yr 2011
\vol 3
\issue 2
\pages 91--98
\mathnet{http://mi.mathnet.ru/ufa97}
\zmath{https://zbmath.org/?q=an:1249.13019}
\transl
\jour Ufa Math. J.
\yr 2011
\vol 3
\issue 2
\pages 89--95
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Уфимский математический журнал
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    Russian version PDF:200
    English version PDF:16
    References:94
    First page:2
     
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