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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Greenspan bound for the order of differential systems


Author: Richard M. Cohn
Journal: Proc. Amer. Math. Soc. 79 (1980), 523-526
MSC: Primary 12H05
MathSciNet review: 572294
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Abstract: Let S be a system of ordinary differential polynomials in indeterminates $ {y_1}, \ldots ,{y_n}$ and of order at most $ {r_i}$ in $ {y_i},1 \leqslant i \leqslant n$. It was shown by J. F. Ritt that if $ \mathfrak{M}$ is a component of S of differential dimension 0, then the order of $ \mathfrak{M}$ is at most $ {r_1} + \ldots + {r_n}$. B. Greenspan improved this bound in the case that every component of S has differential dimension 0. (His work was carried out for difference equations, but is easily transferred to the differential case.) It is shown that the Greenspan bound is valid without this restriction.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0572294-0
PII: S 0002-9939(1980)0572294-0
Keywords: Order of differential systems, differential kernel, Greenspan bound, Jacobi bound
Article copyright: © Copyright 1980 American Mathematical Society