Accession Number:

ADA247314

Title:

The Structure of Finitely Generated Shift-Invariant Spaces in L2(IR(d))

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES

Report Date:

1992-02-01

Pagination or Media Count:

35.0

Abstract:

A simple characterization is given of finitely generated subspaces of L2IRd which are invariant under translation by any multiinteger, 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.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE