WAVELET DECOMPOSITIONS IN $L^2(R^2)$ |
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Authors: | Wu Zhengchang |
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Institution: | Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, China. |
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Abstract: | Let ${V_k}^{+\infinity}_{k=-\infinity}$ be a multiresolution analysis generated by a function $\phi(x)\in L^2(R^2)$. Under this multiresolution framework the key point for studying wavelet decompositions in $L^2(R^2)$ is to study the properties of Wo which is the orthogonal complement of $V_0$ in $V_1:V_1=V_0\oplus W_0$.In this paper the author studies the structure of W_0 and furthermore shows that a box spline of three directions can generate a wavelet decomposition of $L^2(R^2)$. |
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