A Closer Look at Multiresolution Analysis
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.
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