The Determination Of Jumps And The Characterization Of Generators For Multiresolution-Analysis

My thesis consists of four chapters.The subjects of the paper are the detection of edges and the Characterization of frame multiresblution analysis.In chapter 1,we present a short history and background on subjects and the main results.There are two mathematical questions which are proposed in detection of edges:search of(simple) discontinuties and determination of jumps for functions. The aim of Chapters 2 and 3 is to discuss the second question.In Chapter 2 we summarize merits of some ways by which some authors determined values of jumps and establish a criterion on(so-called) advanced concentration factors for determination of jumps which is the mainest result of my paper.In Chapter 3 we discuss the convergence rate for Moricz Process and establish a criterion on concentration factors of Abel-Poisson type.In 1993,Benedetto and Li introduced the notion of frame multiresolution analysis.This is an effective way for construction of affine frames.In Chapter 4 we establish a characterization on generators for frame multireso]ution analysis.