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 APM  Vol.1 No.6 , November 2011
Toeplitz and Translation Operators on the q-Fock Spaces
Fethi Soltani
Abstract: 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 .
Keywords: q-Fock Spaces, q-Exponential Function, q-Derivative Operator, q-Translation Operators, q-Toeplitz Operators, q-Weyl Commutation Relations
Cite this paper: nullF. Soltani, "Toeplitz and Translation Operators on the q-Fock Spaces," Advances in Pure Mathematics, Vol. 1 No. 6, 2011, pp. 325-333. doi: 10.4236/apm.2011.16059.
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