Math @ Duke

Publications [#243835] of Mauro Maggioni
Papers Published
 Maggioni, M, Wavelet frames on groups and hypergroups via discretization of calderón formulas,
Monatshefte fur Mathematik, vol. 143 no. 4
(2004),
pp. 299331 [doi]
(last updated on 2018/02/19)
Abstract: Continuous wavelets are often studied in the general framework of representation theory of squareintegrable representations, or by using convolution relations and Fourier transforms. We consider the wellknown problem whether these continuous wavelets can be discretized to yield wavelet frames. In this paper we use CalderónZygmund singular integral operators and atomic decompositions on spaces of homogeneous type, endowed with families of general translations and dilations, to attack this problem, and obtain strong convergence results for wavelets expansions in a variety of classical functional spaces and smooth molecule spaces. This approach is powerful enough to yield, in a uniform way, for example, frames of smooth wavelets for matrix dilations in ℝn, for an affine extension of the Heisenberg group, and on many commutative hypergroups. © SpringerVerlag 2004.


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