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Some applications of projection operators in wavelets

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By rewriting the projection operatorP 0 in wavelets in another formula, we obtain a characterization of dimJ V0 (x) where V0 is a Γ-shift-invariant subspace ofL 2(R n) derived from a dual wavelet basis and prove that there does not exist a wavelet function ϕ ∈L 2(R) such that\(\hat \psi \) has compact support and ∪ k∈ℤ(supp\(\hat \psi \)+4πk) =R up to a zero subset ofR.

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Bin, H. Some applications of projection operators in wavelets. Acta Mathematica Sinica 11, 105–112 (1995).

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