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TMF, 2012, Volume 171, Number 1, Pages 18–25 (Mi tmf6920)  

This article is cited in 1 scientific paper (total in 1 paper)

Differential operators commuting in the principal part

R. A. Gabieva, A. B. Shabatb

a Aliev Karachai-Cherkess State University, Karachaevsk, Russia
b Landau Institute for Theoretical Physics, Chernogolovka, Moscow Oblast, Russia

Abstract: We consider commuting differential operators with two independent variables of general form and obtain general necessary commutativity conditions for low-order operators. We show that these conditions allow classifying commuting pairs of operators whose coefficients are linear functions of the independent variables.

Keywords: commutative ring of differential operators, Schur's formula, classification

DOI: https://doi.org/10.4213/tmf6920

Full text: PDF file (397 kB)
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English version:
Theoretical and Mathematical Physics, 2012, 171:1, 435–441

Bibliographic databases:

Received: 02.06.2011

Citation: R. A. Gabiev, A. B. Shabat, “Differential operators commuting in the principal part”, TMF, 171:1 (2012), 18–25; Theoret. and Math. Phys., 171:1 (2012), 435–441

Citation in format AMSBIB
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\by R.~A.~Gabiev, A.~B.~Shabat
\paper Differential operators commuting in the~principal part
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  • http://mi.mathnet.ru/eng/tmf6920
  • https://doi.org/10.4213/tmf6920
  • http://mi.mathnet.ru/eng/tmf/v171/i1/p18

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. E. Adler, V. G. Marikhin, A. B. Shabat, “Quantum tops as examples of commuting differential operators”, Theoret. and Math. Phys., 172:3 (2012), 1187–1205  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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