Fock Spaces for the q-Dunkl Kernel

• 作者: Fethi Soltani
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: Generalized q-Fock SPACES q-Dunkl KERNEL q-Dunkl Operator q-Translation OPERATORS
• 年，卷（期）: 2012,（3）
• 页码范围: 169-176
• 页数: 8页
• 分类号: O1

摘要

In this work, we introduce a class of Hilbert spaces of entire functions on the disk , 0<q<1 , with reproducing kernel given by the q-Dunkl kernel . The definition and properties of the space extend naturally those of the well-known classical Fock space. Next, we study the multiplication operator Q by z and the q-Dunkl operator on the Fock space;and we prove that these operators are adjoint-operators and continuous from this space into itself.