The Function Properties Of Several Kinds Of Random Series Represented

In thesis,we study the random entire function?the multivariate random exponen-tial polynomial and the random exponential polynomial by approach of the Residue theorem,Analytic continuation,canonical product and so on,which are the tools from the complex analysis,and combining with some important results of the functional analysis and probability theory.These results extend the existing result.The main content of this thesis is as follows:In chapter one,we introduce the significance and background of this thesis.In chapter two,we discuss the representation of random entire function.We obtain the necessary and sufficient conditions for the existence of the random en-tire function f_w?z?which is bounded in a horizontal band and can be represented by?_n=1^? a_n?w?exp{-?_n?w?z}.In chapter three,we discuss the uniqueness conditions of multiple random analytic function in the weighted Hardy space.The results in chapter two are generalized to several variables.In chapter four,we study the complex random exponential system.A sufficient condition is obtained for the minimality of the complex random exponential system E???w??={ t^ke^?_n?w?t:k = 0,1,2,...,?_n?w?-1;n = 1,2,3,...}in the Banach space.We also prove that each function in the closure of the linear span of exponen-tial system E???w??can be extended to an analytic function represented by a random Taylor-Dirichlet series.