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Exponential and polynomial dichotomies of operator semigroups on Banach spaces

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Schnaubelt R.

Studia Mathematica

2006

tom 175

nr 2

121-138

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.

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1 Studia Mathematica

1 Schnaubelt R.

1 2006

Wyniki wyszukiwania

Exponential and polynomial dichotomies of operator semigroups on Banach spaces