Bargmann Transformation And Its Deformation On General Symmetry Gauss Measure

As we known, S-transformation is a very importation tools in white noise analysis. Bargmann transformation in the finite dimensional Gaussian probability space, the origin of S-transformation, which has fine properties. For instance, it can transform Hermite multinomial into common power function and transform wick integral into common power function, and so on. And theλ-Bargmann transformation, defined by Yuan Shou-cheng, which maintains fundamentally the properties of Bargmann transformation. Fourthermore, it is a bounded operator in the square integrable Gaussian functional space, when the parameter is control in an special area.This thesis focuses on the Bargmann transformation on the general symmetry Gauss measure. By deforming appropriately Bargmann transformation, we get a new transformation that maintains fundamentally the properties of the natural, and also has better properties than the old one. The main work as follows:Firstly, the relations of Bargmann transformation on the general symmetry Gauss measure and Hermite multinomial with respect to Wick integral are discussed.Secondly, the deformation of Bargmann transformation on the general symmetry Gauss measure, that is the Bargmann transformation with parameter, is defined and its relevant properties are established.Finally, Boundedness and Fock denotation of Bargmann transformation on the general symmetry Gauss measure is mainly discussed.