Study Of Some Questions For Wavelet Type Frame

The concept of frame was firstly introduced in by Du?n and Schae?er when theywere studying nonharmonic Fourier series. Every element in a Hilbert space H can berepresented by the frame, but the way of representation is not unique. It also has manyextensivly application in signal processing, image processing, numerical calculation andmany other disciplines. The contents of frame theory chie?y contain two aspects: oneaspect is the research of seeing the frame theory as one direction of function analysis;another aspect is the research of special form frame. this thesis is mainly to study thewavelet type frame and consists of four chapters.Chapter one states the origin of frame concept and sketch the structure and worksof the thesis.Chapter two lists some basic theorem to be used throughout the thesis, and theconcepts of frame, Riesz basis, wavelet type frame and wavelet type bases.Chapter three is one of the main contents. On the basis of known frame perturbationresults, wavelet type frames perturbation results are given from two aspects by propertiesof the wavelet type frames.Chapter four is another main content. we discuss relationship among complement,strong complement, disjoint, strongly disjoint, similar etc, and obtain some results.