Nonlinear SPDEs and Maximal Regularity: An Extended Survey. [PDF]
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A Martingale-Free Introduction to Conditional Gaussian Nonlinear Systems. [PDF]
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On Strongly Continuous Markovian Semigroups
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Stabilized approximations of strongly continuous semigroups
Let \(A\) be the generator of a strongly continuous semigroup \(T(\cdot)\) on a Banach space \(X\) (not necessarily analytic) and let \(V(t) = r(tA)\) be an approximation scheme to the exponential defined by an \(\mathcal{A}\)-stable rational function (such as the backward Euler scheme, the Crank-Nicolson or some Padé approximant). As is well known, an
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On the Asymptotic Behavior of Perturbed Strongly Continuous Semigroups
Mathematische Nachrichten, 2001The author considers a strongly continuous semigroup with generator \(A\) on a Banach space and an \(A\)-bounded perturbation \(B\). He characterizes the norm continuity and compactness of the terms in the Dyson-Phillips series of a perturbed semigroup.
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Distributional chaos for strongly continuous semigroups of operators [PDF]
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Direct integrals of strongly continuous operator semigroups [PDF]
The goal of this article is to develop a theory for direct integrals of $C_0$-semigroups on Hilbert spaces parallel to the recent approach by Lachowicz and Moszyński for direct sums of Banach spaces, diagonal operators, and semigroups. In it we deal with the existence and characterisation of semigroups, asymptotic rates, and questions of ...
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