The Structure of Finitely Generated Shift-Invariant Spaces in L2(IR(d))
Abstract
A simple characterization is given of finitely generated subspaces of L2(IR(d)) which are invariant under translation by any (multi)integer, and used to give conditions under which such a space has a particularly nice generating set, namely a basis, and, more than that, a basis with desirable properties, such as stability, orthogonality, or linear independence. The last property makes sense only for 'local' spaces, i.e., shift-invariant spaces generated by finitely many compactly supported functions, and special attention is paid to such spaces. As an application, we prove that the approximation order provided by a given local space is already provided by the shift-invariant space generated by just one function, with this function constructible as a finite linear combination of the finite generating set for the whole space, hence compactly supported.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1992
- Accession Number
- ADA247314
Entities
People
- Amos Ron
- Carl R. de Boor
- Ronald A. Devore
Organizations
- University of Wisconsin–Madison