Commutative Partial Differential Operators
نویسنده
چکیده
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions that may suggest a theory to be developed. In particular, we address the existence of a “spectral variety” generalizing the spectral curve of the one dimensional theory and the role of the differential resultant.
منابع مشابه
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A method of G. Wilson for generating commutative algebras of ordinary differential operators is extended to higher dimensions. Our construction, based on the theory of D-modules, leads to a new class of examples of commutative rings of partial differential operators with rational spectral varieties. As an application, we briefly discuss their link to the bispectral problem and to the theory of ...
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