## 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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