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PERTURBATION OF WAVELET AND GABOR FRAMES

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Analysis in Theory and Applications 2003年第3期19卷 238-254页

作者： Ivana Carrizo sergio favier Instituto de Matemática Aplicada San Luis Universidad Nacional de San Luis Instituto de Matemática Aplicada San Luis Universidad Nacional de San Luis Av.Ejército de Los Andes 950.5700 San LuisArgentinaAv.Ejército de Los Andes 950.5700 San LuisArgentina

In this work two aspects of theory of frames are presented: a side necessary condition on irregular wavelet frames is obtained, another perturbation of wavelet and Gabor frames is considered. Specifically, we present the results obtained on frame stability when one disturbs the mother of wavelet frame, or the parameter of dilatation, and in Gabor frames when the generating function or the parameter of translation are perturbed. In all cases we work without demanding compactness of the support, neither on the generating function, nor on its Fourier transform.

关键词： Riesz basis Gabor frame wavelet frame perturbation

Maximal Inequalities for the Best Approximation Operator and Simonenko Indices

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Analysis in Theory and Applications 2017年第3期33卷 253-266页

作者： Sonia Acinas sergio favier Instituto de Matematica Aplicada San Luis IMASLUniversidad Nacional de San Luis and CONICETEjercito de los Andes 950D5700HHW San LuisArgentina Departamento de Matematica Facultad de Ciencias Exactas y NaturalesUniversidad Nacional de La PampaL6300CLB Santa RosaLa PampaArgentina Departamento de Matematica Universidad Nacional de San LuisD5700HHW San LuisArgentina

In an abstract set up, we get strong type inequalities in L^p＋1 by assuming weak or extra-weak inequalities in Orlicz spaces. For some classes of functions, the number p is related to Simonenko indices. We apply the results to get strong inequal- ities for maximal functions associated to best Ф-approximation operators in an Orlicz space L^Ф.

关键词： Simonenko indices maximal inequalities best approximation.

IRREGULAR WAVELET FRAMES AND GABOR FRAMES

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Analysis in Theory and Applications 2001年第3期17卷 90-100页

作者： Ole Christensen sergio favier Felipe Zó Department of Mathematics Technical University of DenmarkBuilding 3032800LyngbyDenmark Instituto de Matemática Aplicada San Luis Universidad Nacional de San Luis Consejo Nacional de Investigaciones Científicasy TécnicasAvda.Ejercito de Los Andes950 5700San LuisArgentina

Given g∈L 2(R n ), we consider irregular wavelet for the form $\left\{ {\lambda ^{\frac{n}{2}} g\left( {\lambda _j x - kb} \right)} \right\}_{j\varepsilon zj\varepsilon z^n } ,where\;\lambda _j $ > 0 and b > 0. Sufficient conditions for the wavelet system to constitute a frame for L 2(R n ) are given. For a class of functions g∈L 22(R n ) we prove that certain growth conditions on {λ j } will frames, and that some other types of sequences exclude the frame property. We also give a sufficient condition for a Gabor system $\left\{ {e^{zrib\left( {j,x} \right)} g\left( {x - \lambda _k } \right)} \right\}_{j\varepsilon z^n ,k\varepsilon z} $ to be a frame.

关键词： sufficient condition Stability of Frames Wavelet Transforms Wavelet Frames Riesz Bases