Cyclicity And Completeness Of Exponential System In Some Function Spaces

In this thesis,we deal with the cyclicity of exponential system {e?z} in several function spaces.Moreover,the completeness of system {e?nz} and polynomials with gaps are also being considered.The main contents of this thesis are as follows:The first chapter mainly introduces the background of this thesis and the research status.Meanwhile,we also introduce some propaedeutics and the arrangement of this thesis.In the second ehapter,we discuss the eyclicity of exponential system by quasi analytic method in Ca,where Ca is the weighted Banach space with nonnegative convex weight on the real axis.In the third chapter,we obtain the cyclicity of exponential system in the same way in Hilbert space La2(?).In the fourth chapter,we discuss the same problem for exponential system and justify the completeness of polynomials with gaps by Carleman formula in Fock-type space.In the fifth chapter,we make a brief summary and prospect for this thesis.