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JOURNALS // Matematicheskie Zametki // Archive
Mat. Zametki, 2011 Volume 89, Issue 2, Pages 190–203 (Mi mzm8634)
This article is cited in 10 papers

Hyperbolic Operator Semigroups and Lyapunov's Equation

A. G. Baskakov, A. A. Vorobjev, M. Yu. Romanova

Voronezh State University

Abstract: We obtain necessary and sufficient conditions for the hyperbolicity of a semigroup of operators. In so doing, we use Lyapunov's equation in operator form constructed from its generator.

Keywords: hyperbolic semigroup of operators, Lyapunov's equation, exponential dichotomy, Howland hyperbolic semigroup, Banach algebra, Krein's theorem.

UDC: 517.984+517.986

Received: 17.02.2009

DOI: 10.4213/mzm8634


 English version: Mathematical Notes, 2011, 89:2, 194–205

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© Steklov Math. Inst. of RAS, 2024