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Asymptotic analysis for linear difference equations
Author(s):
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:
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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