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

 

A differentially algebraic replacement theorem, and analog computability


Authors: Leonard Lipshitz and Lee A. Rubel
Journal: Proc. Amer. Math. Soc. 99 (1987), 367-372
MSC: Primary 12H05
Corrigendum: Proc. Amer. Math. Soc. 104 (1988), 668.
MathSciNet review: 870803
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Abstract: A theorem is proved that enables one to replace a $ {C^n}$ solution of a system of algebraic differential equations by analytic solutions nearby, such that each satisfies its own algebraic differential equation. As an application, we emend a proof of the Shannon-Pour-E1 thesis relating the outputs of analog computers to solutions of algebraic differential equations.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0870803-1
PII: S 0002-9939(1987)0870803-1
Article copyright: © Copyright 1987 American Mathematical Society