Two-sided Fourier Transform In Clifford Analysis And Application

In this paper,we study the properties and applications of the two-sided Fourier transformation in Clifford analysis.Clifford analysis is a generalization of complex vari-able function theory to high-dimensional space.It is defined on the vector space R~n and valued in the Clifford algebra.It can be regarded as a generalization of real analysis,complex analysis and quaternion analysis.The Fourier transform is a kind of integral transformation with important theoretical significance and extensive practical applica-tion in complex analysis theory.The Clifford Fourier transform(CFT)is a nontrivial generalization of the classical Fourier transform(FT)using Clifford algebra.In recent years,some achievements have been made in the study of the properties of the two-sided Fourier transform in quaternion analysis,but the study of the two-sided Fourier transform in Clifford analysis is less.In this paper,properties of the two-sided Fourier transforma-tion in Clifford analysis are studied and a solution to the partial differential equation in Clifford analysis is given by using these properties.In chapter 1,we introduce Clifford algebra Cl0,n and function.We also introduce the algorithm of function in Cl0,n.Then we give some definitions and related lemmas which are needed in this paper.In chapter 2,we first give the definition of the two-sided Fourier transform and its inverse transformation on the space of L1(R~n;Cl0,n).Then we study the differential,Plancherel identity,Parseval identity,time-frequency shift and other properties of the two-sided Fourier transformation.In chapter 3,we discuss the uncertainty principle of the two-sided Fourier transform in Clifford analysis and study the application of the two-sided Fourier transform in the partial differential equation.