Nonseparable Radial Frame Multiresolution Analysis in Multidimensions

Abstract

In this article we present a nonseparable multiresolution structure based on frames which is defined by radial frame scaling functions. The Fourier transform of these functions is the indicator (characteristic) function of a measurable set. We also construct the resulting frame multiwavelets, which can be isotropic as well. Our construction can be carried out in any number of dimensions and for a big variety of dilation matrices.

Keywords:

• Nonseparable multiresolution analysis
• Wavelets
• Frames
• 1991 Mathematics Subject Classification: 42C40
• 41A05
• 41A30
• 41A63
• 42C30
• 94A20
• 94A12

Acknowledgment

This research was partially supported by the following grants: University of Houston TLCC funds, NSF-DMS 0070376, NSF Career Award CISE-9985482, NSF-CHE-0074311, by Texas Higher Education Coordinating Board ARP-003652-0071-2001 and R. A. Welch Foundation E-0608. We would also like to thank the anonymous referee for his suggestions.

Notes

^aFollowing Papadakis (2003) ; thus,