Complex symmetric C₀-semigroups on the Fock space

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• 作者：Pham Viet Hai ^{VIETHAI001@e.ntu.edu.sg" class="auth_mail" title="E-mail the corresponding author} ; Le Hai Khoi ; ^{lhkhoi@ntu.edu.sg" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fock space ; Complex symmetry ; Semigroup ; Weighted composition operators
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：445
• 期：2
• 页码：1367-1389
• 全文大小：476 K

文摘

In this paper we introduce a new concept in dynamical systems: the complex symmetric operator C₀$C_0$-semigroups (groups) acting on Hilbert space. Using techniques of weighted composition operators we study these semigroups on the Fock space F²${\mathcal{F}}^2$ and show, in particular, that complex symmetric operator C₀$C_0$-semigroups contain the familiar unitary semigroups as a proper subclass.