Exponential and polynomial dichotomies of operator semigroups on Banach spaces

Roland Schnaubelt

Displaying similar documents to “Exponential and polynomial dichotomies of operator semigroups on Banach spaces”

On the exponential stability and dichotomy of $C_{0}$ -semigroups

Phóng Vũ (1999)

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A characterization of exponentially dichotomic and exponentially stable $C_{0}$ -semigroups in terms of solutions of an operator equation of Lyapunov type is presented. As a corollary a new and shorter proof of van Neerven’s recent characterization of exponential stability in terms of boundedness of convolutions of a semigroup with almost periodic functions is given.

A sharp result on the exponential operator-norm decay of a family of strongly continuous semigroups.

R. Triggiani (1994)

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Linear neutral partial differential equations: A semigroup approach.

Nagel, Rainer, Nguyen Thieu Huy (2003)

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Mild integrated C-existence families

Shen Wang (1995)

Studia Mathematica

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We study mild n times integrated C-existence families without the assumption of exponential boundedness. We present several equivalent conditions for these families. Hille-Yosida type necessary and sufficient conditions are given for the exponentially bounded case.

Functional calculi, regularized semigroups and integrated semigroups

Ralph deLaubenfels, Mustapha Jazar (1999)

Studia Mathematica

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We characterize closed linear operators A, on a Banach space, for which the corresponding abstract Cauchy problem has a unique polynomially bounded solution for all initial data in the domain of $A^{n}$ , for some nonnegative integer n, in terms of functional calculi, regularized semigroups, integrated semigroups and the growth of the resolvent in the right half-plane. We construct a semigroup analogue of a spectral distribution for such operators, and an extended functional calculus: When...