Toeplitz and Translation Operators on the q-Fock Spaces  

作　　者：Fethi Soltani 

机构地区：[1]不详

出　　处：《Advances in Pure Mathematics》2011年第6期325-333,共9页理论数学进展（英文）

摘　　要：In this work, we introduce a class of Hilbert spaces Fq of entire functions on the disk , , with reproducing kernel given by the q-exponential function eq(z);and we prove some properties concerning Toeplitz operators on this space. The definition and properties of the space extend naturally those of the well-known classical Fock space. Next, we study the multiplication operator Dq by and the q-Derivative operator on the Fock space Fq;and we prove that these operators are adjoint-operators and continuous from this space into itself. Lastly, we study a generalized translation operators and a Weyl commutation relations on Fq .In this work, we introduce a class of Hilbert spaces Fq of entire functions on the disk , , with reproducing kernel given by the q-exponential function eq(z);and we prove some properties concerning Toeplitz operators on this space. The definition and properties of the space extend naturally those of the well-known classical Fock space. Next, we study the multiplication operator Dq by and the q-Derivative operator on the Fock space Fq;and we prove that these operators are adjoint-operators and continuous from this space into itself. Lastly, we study a generalized translation operators and a Weyl commutation relations on Fq .

关 键 词：q-Fock Spaces q-Exponential Function Q-DERIVATIVE Operator q-Translation OPERATORS q-Toeplitz OPERATORS q-Weyl Commutation Relations 

分 类 号：O1[理学—数学]