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Multiresolution analysis and Radon measures on a locally compact Abelian group
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 4, pp. 859-871 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 22B99, 28A33, 43A15
Keywords: multiresolution analysis; Radon measures; topological groups 
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Galindo, Félix; Sanz, Javier. Multiresolution analysis and Radon measures on a locally compact Abelian group. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 4, pp. 859-871. http://geodesic.mathdoc.fr/item/CMJ_2001_51_4_a13/

[1] J. Diestel and J. J. Uhl, Jr.: Vector Measures. Mathematical Surveys, Number 15, AMS. Providence, Rhode Island, 1977. | MR

[2] N.  Dunford and J. T.  Schwartz: Linear Operators. Part I: General Theory. Wiley Interscience, New York, 1988. | MR

[3] R. E. Edwards and G. I. Gaudry: Littlewood-Paley and Multiplier Theory. Springer-Verlag, Berlin, 1977. | MR

[4] F. Galindo: Procesos semiperiódicos multidimensionales. Multiplicadores y funciones de transferencia. Ph.D. Thesis, Universidad de Valladolid, Valladolid, 1995.

[5] E. Hewitt and K. A. Ross: Abstract Harmonic Analysis I. Springer-Verlag, Berlin, 1963.

[6] E.  Hewitt and K. A.  Ross: Abstract Harmonic Analysis II. Springer-Verlag, Berlin, 1970. | MR

[7] W. C.  Lang: Orthogonal wavelets on the Cantor dyadic group. SIAM J.  Math. Anal. 27 (1996), 305–312. | DOI | MR | Zbl

[8] R.  Larsen: An Introduction to the Theory of Multipliers. Springer-Verlag, Berlin, 1971. | MR | Zbl

[9] P. G.  Lemarié: Base d’ondelettes sur les groupes de Lie stratifiés. Bull. Soc. Math. France 117 (1989), 211–232. | DOI | MR

[10] S. G.  Mallat: Multiresolution approximations and wavelet orthonormal bases of $L^2(\mathbb{R})$. Trans. Amer. Math. Soc. 315 (1989), 69–87. | MR | Zbl

[11] Y.  Meyer: Wavelets and operators. Cambridge University Press, Cambridge, 1992. | MR | Zbl

[12] M.  Núñez: Multipliers on the space of semiperiodic sequences. Trans. Amer. Math. Soc. 291 (1984), 801–811. | MR

[13] G. E. Shilov and B. L.  Gurevich: Integral, Measure and Derivative: a unified approach. Dover, New York, 1977. | MR