Asymptotic analysis for linear difference equations |
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| Authors: | Katsunori Iwasaki |
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| Affiliation: | Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153 Japan |
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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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| Keywords: | Difference equation profile operator factorial asymptotic expansion Gevrey estimate |
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