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Proceedings of the American Mathematical Society

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Perturbations of the Haar wavelet by convolution


Authors: H. A. Aimar, A. L. Bernardis and O. P. Gorosito
Journal: Proc. Amer. Math. Soc. 129 (2001), 3619-3621
MSC (2000): Primary 42C40
Published electronically: April 24, 2001
MathSciNet review: 1860495
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Abstract: In this note we show that the standard convolution regularization of the Haar system generates Riesz bases of smooth functions for $L^2(\mathbb R)$, providing in this way an alternative to the approach given by Govil and Zalik [Proc. Amer. Math. Soc. 125 (1997), 3363-3370].


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Additional Information

H. A. Aimar
Affiliation: IMAL (CONICET), Güemes 3450, (3000) Santa Fe, Argentina
Email: haimar@ceride.gov.ar

A. L. Bernardis
Affiliation: IMAL (CONICET), Güemes 3450, (3000) Santa Fe, Argentina
Email: bernard@ceride.gov.ar

O. P. Gorosito
Affiliation: Departamento de Matemática, Facultad de Ingeniería Química, Universidad Nacional del Litoral, Santiago del Estero 2829, (3000) Santa Fe, Argentina
Email: ogoro@fiqus.unl.edu.ar

DOI: https://doi.org/10.1090/S0002-9939-01-05939-1
Keywords: Riesz bases, Haar wavelets, basis perturbations.
Received by editor(s): January 11, 2000
Received by editor(s) in revised form: April 20, 2000
Published electronically: April 24, 2001
Additional Notes: This research was supported by CONICET and Proy. CAI+D - UNL
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2001 American Mathematical Society