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On commuting differential operators in two-dimensionality. (Russian. English summary) Zbl 1249.13019
Authors’ abstract: A generalization to the multi-dimensional case of commutative rings of differential operators is considered. An algorithm for the construction of commuting two-dimensional differential operators is formulated for a special kind of operators related to the simple one-dimensional model proposed by J. L. Burchnall and T. W. Chaundy [Proc. R. Soc. Lond., Ser. A 134, 471–485 (1931; Zbl 0003.25701)]. 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.
MSC:
13N10 Commutative rings of differential operators and their modules
Citations:
Zbl 0003.25701
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