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V. Bargmann, “On a Hilbert Space of Analytic Functions and an Associated Integral Transform, Part I,” Communications on Pure and Applied Mathematics, Vol. 14, No. 3, 1961, pp. 187-214. doi:10.1002/cpa.3160140303

has been cited by the following article:

• TITLE: Toeplitz and Translation Operators on the q-Fock Spaces

  AUTHORS: Fethi Soltani

  KEYWORDS: q-Fock Spaces, q-Exponential Function, q-Derivative Operator, q-Translation Operators, q-Toeplitz Operators, q-Weyl Commutation Relations

  JOURNAL NAME: Advances in Pure Mathematics, Vol.1 No.6, November 24, 2011

  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 .