Multiresolution analysis (MRA) on a compact abelian group G has been constructed with epimorphism as a dilation operator. We show a characterization of scaling sequences of an MRA on $L^p(G)$, $1\le p<\infty$. With the help of the scaling sequence we construct an orthonormal wavelet basis of $L^2(G)$.

中文翻译：

---

紧凑型阿贝尔群上的小波

构造了一个紧凑的阿贝尔群G的多分辨率分析（MRA），并将其作为扩张算子。我们展示了MRA的缩放序列的特征${\mathrm{大号}}^p（G）$， $\mathrm{1个}\le p<\infty$。借助定标序列，我们构建了正交小波基${\mathrm{大号}}^2（G）$。