Continuous and localized Riesz bases for spaces defined by Muckenhoupt weights

Aimar, Hugo Alejandro
Ramos, Wilfredo Ariel

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Publication date

October 2015

DOI

10.1016/j.jmaa.2015.05.003

Publisher

Elsevier BV

ISSN

0022-247X

Journal

Journal of Mathematical Analysis and Applications

Abstract

Let w be an A∞-Muckenhoupt weight in R. Let L2(wdx) denote the space of square integrable real functions with the measure w(x)dx and the weighted scalar product f, g w = R f g wdx. By regularization of an unbalanced Haar system in L2(wdx) we construct absolutely continuous Riesz bases with supports as close to the dyadic intervals as desired. Also the Riesz bounds can be chosen as close to 1 as desired. The main tool used in the proof is Cotlar’s Lemma.Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada ; ArgentinaFil: Ramos, Wilfredo Ariel. Universidad Nacional del Nordeste. Facultad de Cs.exactas Naturales y Agrimensura. Departamen...