Perturbation Of Frames And Explicit Structuer Of Wavelet Tight Frames

This paper mainly contains four parts.In the first chapter,we firstly introduce the definations of stability of frame pertubation and generalized frame , and we look back on the history of Paley-Wiener theorem,then we generalize the Paley-Wiener theorem 1.c to the generalized frame,so we obtain theorem 1.1.In the second chapter.we firstly estimate Riesz bounds of the Kadec's 1/4 theorem of R. Young by theorem 2.c and theorem 2.e, then we generalize 1/4 theorem of Wenchang Sun and Xingwei Zhou,that is, we generalize the conclusion from real number sequence to complex number sequ-ence.On the basis of this,we introduce the defination of frame sequence, and give the sufficient condition of stability of frame sequence pertubation .In the third chapter,we firstly generalize the necessary and sufficient condition of Gabor frame with compact support of I.Daubichies from spanning frame of single monther wavelet to spanning frame of many mother wavelets,then we generalize the conclusion on the Gabor frame with compact support of Zhang Jing, so we obtain a conclusion on pertubation of mother wav-elet.Anther we give sufficient conditions of single sample value pertubation and several sample values pertubation.In the fourth chapter,we generalize the conclusions of Lihong Cun and Zhengxing Cheng,that is, we generalize the explicit structuer of wavelet tight frame from 3-band to any odd band. And,we give the decomposition and recnstrustion formulas of wavelet tight frame which are similar to those of orthonormal wavelets.In the following we display the main results in this dissertation.