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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Asymptotic analysis for
linear difference equations


Author: Katsunori Iwasaki
Journal: Trans. Amer. Math. Soc. 349 (1997), 4107-4142
MSC (1991): Primary 39A10, 39A12, 40A05, 46M20
MathSciNet review: 1401775
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Abstract: We are concerned with asymptotic analysis for linear difference equations in a locally convex space. First we introduce the profile operator, which plays a central role in analyzing the asymptotic behaviors of the solutions. Then factorial asymptotic expansions for the solutions are given quite explicitly. Finally we obtain Gevrey estimates for the solutions. In a forthcoming paper we will develop the theory of cohomology groups for recurrence relations. The main results in this paper lay analytic foundations of such an algebraic theory, while they are of intrinsic interest in the theory of finite differences.


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Additional Information

Katsunori Iwasaki
Affiliation: Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153 Japan
Address at time of publication: Department of Mathematics, Kyushu University, G-10-1 Hakozaki, Higashi-ku, Fukuoka 812-81 Japan
Email: iwasaki@ms.u-tokyo-ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01849-7
PII: S 0002-9947(97)01849-7
Keywords: Difference equation, profile operator, factorial asymptotic expansion, Gevrey estimate
Received by editor(s): October 31, 1994
Received by editor(s) in revised form: March 18, 1996
Article copyright: © Copyright 1997 American Mathematical Society