Let G be a second countable locally compact abelian group, L be a uniform lattice in G and \(S_L\) be a fundamental domain for L in G. Let \(L_{\circ }^p(G)= \{ \varphi : G \longrightarrow {\mathbb {C}};\quad \big \Vert \sum _{k\in L}|\varphi (k^{-1}x)|\big \Vert _{L^p(S_L)} < \infty \}\) \((1\leqslant p\leqslant \infty )\). In this paper we aim among other things, to introduce the Banach space \(L_{\circ }^p(G)\) \((1\leqslant p\leqslant \infty )\), with the norm \(|\cdot |_p\), and for \(p=2\) and a refinable function \(\varphi \in L_{\circ }^2(G)\) and the Riesz family generated by the shifts of \(\varphi\) by L in G, construct a multiresolution analysis in L²(G). Also some examples are provided to support our construction.

令G是第二个可数局部紧致阿贝尔群，L是G中的均匀格，\(S_L\)是G中L的基本域。令\(L_{\circ }^p(G)= \{ \varphi : G \longrightarrow {\mathbb {C}};\quad \big \Vert \sum _{k\in L}|\varphi (k ^{-1}x)|\big \Vert _{L^p(S_L)} < \infty \}\) \((1\leqslant p\leqslant \infty )\)。在本文中，我们的目标之一是引入 Banach 空间\(L_{\circ }^p(G)\) \((1\leqslant p\leqslant \infty )\)，规范\(|\ cdot |_p\)，对于\(p=2\)和一个可细化的函数 \(\varphi \in L_{\circ }^2(G)\)和由\(\varphi\)通过L in G的移位生成的 Riesz 族，在L ² ( G )中构建多分辨率分析。还提供了一些例子来支持我们的建设。