### Some Applications of Projection Operators in Wavelets

### Bin Han

## Abstract

By rewriting the projection operator $P_0$ in wavelets in another
formula, we obtain
a characterization of dim$J_{V_0}(x)$ where $V_0$ is a
$\Gamma$-shift-invariant subspace of $L^2(R^n)$ derived from a dual
wavelet basis and prove that there does not exist a wavelet function
$\psi\in L^2(R)$ such that $\hat
\psi$ has compact support and $\cup_{k \in \Z}(\text{supp}\hat\psi+4\pi
k)=R $ up to a zero subset of $R$.

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