Some applications of projection operators in wavelets.

By rewriting the projection operator P in wavelets in another formula, we obtain a characterization of dim J ( x) where V is a Γ-shift-invariant subspace of L( R) derived from a dual wavelet basis and prove that there does not exist a wavelet function ϕ ∈ L( R) such that $$\hat \psi $$ has compact support and ∪(supp $$\hat \psi $$ +4 πk) = R up to a zero subset of R. [ABSTRACT FROM AUTHOR]