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Titlebook: Semigroups of Operators -Theory and Applications; Będlewo, Poland, Oct Jacek Banasiak,Adam Bobrowski,Mirosław Lachowicz Conference proceedi

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The Evolution of Operator Semigroupsverse applications to many areas of mathematics and science developed rapidly. The theory was based on two main results, the wellposedness theorem and the generation theorem. By the early 1970s, analogues of these two theorems were developed for semigroups of nonlinear operators. Since then, extensi
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On Strong Convergence to Ergodic Projection for Perturbed Substochastic Semigroupsgroup generated by . We show that if some remainder term . of the Dyson-Phillips expansion of . depends continuously on . in the uniform topology then . converges strongly to its ergodic projection as .. The proof relies on a “0–2” law for .-semigroups by G. Greiner. We characterize also the existen
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On Robustness of Strongly Stable Semigroups with Spectrum on ,generator of the unperturbed semigroup has a finite spectral point on the imaginary axis and the resolvent operator is polynomially bounded elsewhere on the imaginary axis. As our main result we present conditions for preservation of the strong stability of the semigroup under bounded perturbations.
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Uniform Stabilization with Arbitrary Decay Rates of the Oseen Equation by Finite-Dimensional Tangentypes of ‘tangential’ controls: (i) a (Dirichlet-type) tangential boundary control acting on an arbitrarily small open sub-portion . of positive measure of the full boundary .; and (ii) an interior control acting tangentially on a localized collar of the boundary supported on .. The main result of th
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Two Approaches to Infinite Dimensional Extension of Feynman-Kac Theorem Hilbert spaces ., . with an .-valued .-Wiener process .: ., ., . and solutions to the infinite dimensional deterministic Cauchy problem ., ., . for the probability characteristic . with a measurable . is under consideration. The main point of the paper is studying the relationship on the basis of t
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