Exponential Operators and Hermite Type Polynomials

This thesis consists of five Chapters. Chapter 1 is devoted to the Introduction. We investigate some basic properties of the exponential operators, in Chapter 2. Chapter 3, gives the proves of some exponential operator identities such as Weyl, Sack, Hausdorff and Crofton identities. In Chapter 4, we study the monomiality principle and its properties. Finally in the last chapter, as an application to Chapters 3 and 4, we investigate some properties of Hermite polynomials in two variables, Hermite-Kampe de Feriet polynomials, Laguerre polynomials in two variables and Hermite-Based Appell polynomials. Keywords: Exponential operators,Weyl, Sack, Hausdorff and Crofton identities, Monomiality principle,Hermite-Kampe de Feriet polynomials, Laguerre polynomials in two variables.