Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
multiresolution analysis; Radon measures; topological groups
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
[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 0262773
[7] W. C. Lang: Orthogonal wavelets on the Cantor dyadic group. SIAM J. Math. Anal. 27 (1996), 305–312. DOI 10.1137/S0036141093248049 | MR 1373159 | Zbl 0841.42014
[8] R. Larsen: An Introduction to the Theory of Multipliers. Springer-Verlag, Berlin, 1971. MR 0435738 | Zbl 0213.13301
[9] P. G. Lemarié: Base d’ondelettes sur les groupes de Lie stratifiés. Bull. Soc. Math. France 117 (1989), 211–232. DOI 10.24033/bsmf.2118 | MR 1015808
[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
[11] Y. Meyer: Wavelets and operators. Cambridge University Press, Cambridge, 1992. MR 1228209 | Zbl 0776.42019
[12] M. Núñez: Multipliers on the space of semiperiodic sequences. Trans. Amer. Math. Soc. 291 (1984), 801–811. MR 0800264
[13] G. E. Shilov and B. L. Gurevich: Integral, Measure and Derivative: a unified approach. Dover, New York, 1977. MR 0466463
Search
Partner of
