Complex Symmetric C0-semigroups on A2(C+) |
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Authors: | Kai Kai HAN Mao Fa WANG |
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Institution: | 1.School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, P. R. China;2.School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China |
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Abstract: | In this paper, we study complex symmetric C0-semigroups on the Bergman space A2(C+) of the right half-plane C+. In contrast to the classical case, we prove that the only involutive composition operator on A2(C+) is the identity operator, and the class of J-symmetric composition operators does not coincide with the class of normal composition operators. In addition, we divide semigroups {ψt} of linear fractional self-maps of C+ into two classes. We show that the associated composition operator semigroup {Tt} is strongly continuous and identify its infinitesimal generator. As an application, we characterize Jσ-symmetric C0-semigroups of composition operators on A2(C+). |
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Keywords: | C0-semigroup Bergman space composition operator complex symmetry |
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