Asymptotic Behaviour of Convolution Semigroups |
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Authors: | Maren Schmalmack |
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Institution: | (1) Institut fur Mathematik, Universitat Hannover, Welfengarten 1 D-30167 Hannover, Germany |
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Abstract: | In this paper, necessary and sufficient conditions are
given for U * μ*n to converge uniformly on the real axis; here $\mu$ is a nonsingular probability measure on ℝ, and U is a Banach space valued
L∞-function. A connection to uniform convergence of Cesaro mean values is shown. By applying the results to extended orbits
of bounded C_0-semigroups on a Banach space X one can relate both kernel and range of the respective generator with those
of the derivative operator on L∞(X). Ergodic theorems and consequences for subordinated semigroups, in particular for holomorphic semigroups, are deduced. |
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Keywords: | |
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