Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4586981 | Journal of Algebra | 2010 | 17 Pages |
Abstract
We first study some properties of images of commuting differential operators of polynomial algebras of order one with constant leading coefficients. We then propose what we call the image conjecture on these differential operators and show that the Jacobian conjecture (Bass et al. (1982) [BCW], , van den Essen (2000) [E], , de Bondt (2009) [Bo], ) (hence also the Dixmier conjecture (Dixmier (1968) [D], )) and the vanishing conjecture (Zhao (2007) [Z3]) of differential operators with constant coefficients are actually equivalent to certain special cases of the image conjecture. A connection of the image conjecture, and hence also the Jacobian conjecture, with multidimensional Laplace transformations of polynomials is also discussed.
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Physical Sciences and Engineering
Mathematics
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