Equations For Parseval's Frame Wavelets In L²(\R^d) With Compact Supports

2016/07/31 by Dai, Xingde
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1608.00208

Abstract

Let d≥ 1 be a natural number and A₀ be a d× d expansive integral matrix with determinant ± 2. Then A₀ is integrally similar to an integral matrix A with certain additional properties. A finite solution to the system of equations associated with the matrix A will result in an iterated sequence \Ψ^k χ_[0,1)^d\ that converges to a function φ_A in L²(\R^d)-norm. With this (scaling) function φ_A, we will construct the Parseval's wavelet function ψ with compact support associated with matrix A₀.

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