Fourier Analysis of the Approximation Power of Principal Shift-Invariant Spaces
Abstract
Spaces spanned by finitely or countably many translates of one or several basic functions play an important role in spline theory, radial basis function theory, sampling theory and wavelet theory. Spline theory stresses the case when the basic functions are compactly supported, while sampling theory single out the case when the spectrum (i.e., the support of the Fourier transform) of the basic functions is compact. In the radial basis function theory, neither of these is assumed, and instead, the computational simplicity as well as the positive definiteness (i.e., the positivity of the Fourier transform) of the basic functions is preferred. Finally, wavelet theory focuses on the interrelation between the initial space and its dyadic dilates. In all these areas, the underlying space is meant for approximation or decomposition of functions, and thus, the determination of its approximation properties is of basic significance.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1991
- Accession Number
- ADA246713
Entities
People
- Amos Ron
- Carl R. de Boor
Organizations
- University of Wisconsin–Madison