Continuous wavelet transform in L~2(R~n)
Rui Zhao · Jounal of Xidian University · 2002
The continuous wavelet transform is discussed in L 2(R n) and the reconstruction formula produced by the transform function and that produced by the function which is different from the transform function are obtained. The conditions which make these reconstruction formulae true in the strong topology are obtained and the condition which makes the reconstruction formula produced by the function which is different from the transform function true is the generalization of the condition which makes the reconstruction formula produced by the transform function true. Let n= 1,and the condition that makes the reconstruction formula produced by the function which is different from the transform function true in L 2(R) is obtained. By comparison with Daubechiess results, the conditions for the transform function and those for the function which produces the reconstruction formula are fewer, thus expanding the applications of the reconstruction formula of the continuous wavelet transform.