Operator Relations, Dynamical Systems, and Representations of a Class of Wick Algebras
We consider families of operators satisfying a general class of relations, whose solutions can be described in terms of orbits of some dynamical system acting on the spectrum of a commuting sub-family. In the first section we introduce a class of relations and show, how the representations of such relations are related to orbits of the corresponding dynamical system. Also, we discuss the problem of accurate sense of the relation for unbounded operators. In Section 2, we study the class of *-algebras allowing Wick ordering whose representations can be studied by using methods of Section 1. We classify such Wick *-algebras, and discuss their representations.
Abstract Kim et al. (Appl. Math. Inf. Sci. 9(6):1-6, 2015) consider the q -extensions of Boole polynomials. In this paper, we consider Witt-type formula for the q -Boole polynomials with weights and derive some new interesting identities and properties of those polynomials and numbers from the Witt-type formula which are related to special polynomials and numbers.