Some Results Of Complex Equiangular Tight Frames

In 1952,Duffin and Schaffer introduced the concept of frame for Hilbert space in order to study some further problems in nonharmonic Fourier series.Today,frame has been widely used in wavelet analysis,signal processing,image processing,data compression, sampling theorems,numberical calculation,theory of function space,and so on.This thesis is mainly to discuss the theory of complex equiangular tight frame for Hilbert space.The content consists of four parts.Chapter 1 summarizes the emergence and development of frame and equiangular tight frame,and sketches the main work and the structure of the thesis.Chapter 2 introduces the concepts and some basic properties of general frame and Grassmannian frame.Chapter 3 studies some problems of the complex equiangular tight frame for Hilbert space.At first,some properties and judging methods of equiangular tight frame are given. Secondly,some results of real equiangular tight frame are extended to complex equiangular tight frame.The final chapter is a summary of this thesis and puts forward the vision for future research.