Some Problem About Parseval Frame Wavlets

The theory of frames for a Hilbert space plays a fundamental role in signal processing,image processing,data compression,robust data transmission and more.In thetheory of frames,Parseval frame wavelets is one of the extensive realms which need mostto develop with thorough research.In this paper,we focus on these problems:1.The existance of Parseval frame wavelets,which is MRA,non-W₀-frame andker((?))={0}.2.The existance of Parseval frame wavelets,which is not MRA,non-W₀-frame andker(?)={0}.3.The existance of Parseval frame wavelets,which is not MRA,W₀-frame andker((?))={0}.4.For any given n∈N,the existance of Parsevl frame wavelets,whose dimensionfunction takes vaule 0,1,2...n on some positive measurable sets.5.For any given q/p∈(0,1),the existance of Parseval frame wavelets,whose dimension function takes vaule q/p on some positive measurable sets.