Exponential and polynomial dichotomies of operator semigroups on Banach spaces

• Autorzy: Roland Schnaubelt
• Języki publikacji: EN

Abstrakty

EN

Let A generate a C₀-semigroup T(·) on a Banach space X such that the resolvent R(iτ,A) exists and is uniformly bounded for τ ∈ ℝ. We show that there exists a closed, possibly unbounded projection P on X commuting with T(t). Moreover, T(t)x decays exponentially as t → ∞ for x in the range of P and T(t)x exists and decays exponentially as t → -∞ for x in the kernel of P. The domain of P depends on the Fourier type of X. If R(iτ,A) is only polynomially bounded, one obtains a similar result with polynomial decay. As an application we study a partial functional differential equation.

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 175
• Numer: 2
• Strony: 121-138

Daty

wydano

2006

Twórcy

autor

Roland Schnaubelt

• FB Mathematik und Informatik, Martin-Luther-Universität, 06099 Halle, Germany

Identyfikatory

DOI

10.4064/sm175-2-2