A Closer Look at Multiresolution Analysis
Ole Christensen · Applied and numerical harmonic analysis · 2010
In this chapter we provide the technical details in the construction of a wavelet orthonormal basis for L 2 ( $$\mathbb R$$ ) In Section 9.1 we prove a few immediate consequences of the conditions in a multiresolution analysis. Section 9.2 proves several results concerning the spaces V j and W j , and the construction of a wavelet is presented in Section 9.3. Finally, Section 9.4 proves that the conditions in Theorem 8.2.11 are sufficient for a function φ to generate a multiresolution analysis.