Accession Number : ADA304489

Title :   Stability and Independence of the Shifts of Finitely Many Refinable Functions.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES

Personal Author(s) : Hogan, Thomas A.

PDF Url : ADA304489

Report Date : FEB 1996

Pagination or Media Count : 24

Abstract : Typical constructions of wavelets depend on the stability of the shifts of an underlying refinable function. Unfortunately, several desirable properties are not available with compactly supported orthogonal wavelets, e.g. symmetry and piecewise polynomial structure. Presently, multiwavelets seem to offer a satisfactory alternative. The study of multiwavelets involves the consideration of the properties of several (simultaneously) refinable functions. In Section 2 of this paper, we characterize stability and linear independence of the shifts of a finite refinable function set in terms of the refinement mask. Several illustrative examples are provided. The characterizations given in Section 2 actually require that the refinable functions be minimal in some sense. This notion of minimality is made clear in Section 3, where we provide sufficient conditions on the mask to ensure minimality. The conditions are shown to be also necessary under further assumptions on the refinement mask. An example is provided illustrating how the software package MAPLE can be used to investigate at least the case of two simultaneously refinable functions.

Descriptors :   *MAPPING(TRANSFORMATIONS), LINEAR SYSTEMS, STABILITY, MATRICES(MATHEMATICS), RESOLUTION, EIGENVECTORS, APPROXIMATION(MATHEMATICS), SHIFTING, POLYNOMIALS, PERIODIC FUNCTIONS.

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE