# Article

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Keywords:
multiresolution analysis; Radon measures; topological groups
Summary:
A multiresolution analysis is defined in a class of locally compact abelian groups $G$. It is shown that the spaces of integrable functions $\mathcal L^p(G)$ and the complex Radon measures $M(G)$ admit a simple characterization in terms of this multiresolution analysis.
References:
[1] J. Diestel and J. J. Uhl, Jr.: Vector Measures. Mathematical Surveys, Number 15, AMS. Providence, Rhode Island, 1977. MR 0453964
[2] N.  Dunford and J. T.  Schwartz: Linear Operators. Part I: General Theory. Wiley Interscience, New York, 1988. MR 1009162
[3] R. E. Edwards and G. I. Gaudry: Littlewood-Paley and Multiplier Theory. Springer-Verlag, Berlin, 1977. MR 0618663
[10] S. G.  Mallat: Multiresolution approximations and wavelet orthonormal bases of $L^2(\mathbb{R})$. Trans. Amer. Math. Soc. 315 (1989), 69–87. MR 1008470 | Zbl 0686.42018