2-dilation Fourier Multipliers For Orthogonal Multi-Wavelets In L~2(R)and It's Applications

In this paper,we mainly discussed the problem of the 2-dilation Fourier Multipliers for Orthogonal Multi-wavelets in the one-dimensional real space R.First,the 2-dilation Fourier Multipliers for Orthogonal Multi-wavelets to be the constant matrix was discussed as an example.The necessary and sufficient conditions for a special case is given.On this basis and through the study of the property of the 2-dilation Orthogonal Multi-wavelets in one-dimensional real space,the three sufficient conditions for the 2-dilation Fourier Multipliers for Orthogonal Multi-wavelets were given and proved.This provided us with a theory to construct some new wavelets.Secondly,combining the knowledge of algebraic theory and the properties of the unitary matrix,We obtain the conclusion of 2-dilation Fourier Multipliers for Orthogonal Multi-wavelets are Unitary matrix.Finally,as an application,some 2-dilation Orthogonal Multi-wavelets are constructed.