Geodesic
A necessary and sufficient condition for the existence of a father wavelet
Studia Mathematica, Tome 114 (1995) no. 3, pp. 207-226 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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It is proved that if ${2^{-m/2} ψ(2^{-m} • - k)}_{m,k ∈ ℤ}$ is an orthonormal basis in $L^2(ℝ;ℂ)$, then the mother wavelet ψ is obtained from a multiresolution generated by a father wavelet if and only if $∑_{p=1}^{∞| ∑_{k ∈ ℤ} |ψ̂(2^{p}(• + k))|^2 > 0$ a.e.
DOI : 10.4064/sm-114-3-207-226
Keywords: wavelet, multiresolution, existence 
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Gustaf Gripenberg. A necessary and sufficient condition for the existence of a father wavelet. Studia Mathematica, Tome 114 (1995) no. 3, pp. 207-226. doi: 10.4064/sm-114-3-207-226

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