Measures, densities and diameters of frequency bands of scaling functions and wavelets

Authors:
Zhihua Zhang
Affiliations:
Department of Mathematics, University of California, Davis, California 95616, USA
Venue:
Journal of Approximation Theory
Year:
2007

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Journal of Approximation Theory

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Abstract

We investigate the measures of frequency bands of scaling functions and wavelets, and solve an open problem. Furthermore, we give conditions for which the measures of frequency bands of scaling functions are less than 8@p3 and the measures of frequency bands of wavelets are less than 4@p. We also discuss the densities around the origin and the diameters of frequency bands of scaling functions and wavelets, and show that there are essential differences between the single and multidimensional cases.