Construction of Compactly Supported Wavelets Bases of Dilation Factor a for L~2(R)
Hongliang Dai · Hainan Daxue xuebao. Ziran kexue ban · 2006
A pair of compactly supported refinable functions and in L~2(R) was given,when it satisfied a very mild condition,a wavelet ψ of dilation factor a was created and the wavelets ψ_(jk)=a~(j/2)ψ(a~j·-k)(j,kZ) form a Riesz basis for L~2(R).Consequently,{ψ_(jk):j,kZ} is a wavelet basis for L~2(R).