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Asymptotic Behavior of Solutions of Evolution Equations and the Construction of Holomorphic Retractions

โœ Scribed by Victor Khatskevich; Simeon Reich; David Shoikhet

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
402 KB
Volume
189
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

We first study the asymptotic behavior of nonlinear semigroups with holomorphic generators, and then use our results, inter alia, to construct holomorphic retractions onto the fixed point sets of holomorphic self-mappings of bounded convex domains in a complex Banach space.

(*> Ker(I -F'(a)) @ Im ( I -F'(a)) = X .

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In this paper we present a theorem on asymptotic behavior of \(W(n, x(n))\) where \(x(n)\) is a solution of the difference equation \(x(n+1)=f(n, x(n)), n \in N^{+}\)and \(W(n, x): N^{+} \times R^{d} \rightarrow R^{+}\)is continuous. As applications we discuss examples which cannot be handled by the