Accession Number : ADA290147

Title :   Multivariate Wavelet Representations and Approximations.

Descriptive Note : Final technical rept. 1 Jun 90-31 May 94,

Corporate Author : CONNECTICUT UNIV STORRS DEPT OF MATHEMATICS

Personal Author(s) : Madych, Wolodymyr ; Grochenig, K.

PDF Url : ADA290147

Report Date : OCT 1994

Pagination or Media Count : 84

Abstract : The following work has been completed: The recovery of irregularly samples band-limited functions via tempered spline. Band limited functions can be recovered from their values on certain irregularly distributed discrete sampling sets as the limits of the piecewise polynomial spline interpolants when the order of the splines goes to infinity. This significant extension of the classical case when the sampling set is a lattice which was considered by L. Collatz, W. Quade, I. J. Schoenberg, and others. Orthogonalitv criteria for compactly supported scaling functions. The question of whether the integer translates of the scaling function constructed from a prescribed scaling sequency in the standard way are mutually orthogonal is quite subtle. The various conditions and the supporting arguments which are currently in the literature are very complicated. (AN)

Descriptors :   *MULTIVARIATE ANALYSIS, *APPROXIMATION(MATHEMATICS), ALGORITHMS, MATRICES(MATHEMATICS), TRANSFORMATIONS(MATHEMATICS), POLYNOMIALS, INTERPOLATION, SCALING FACTOR, SAMPLING, FOURIER ANALYSIS, CUBIC SPLINE TECHNIQUE.

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE