Multivariate Wavelet Representations and Approximations.

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)

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1994
Accession Number
ADA290147

Entities

People

  • K. Grochenig
  • Wolodymyr Madych

Organizations

  • University of Connecticut

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Analogs
  • Birds
  • Difference Equations
  • Differential Equations
  • Equations
  • Fourier Analysis
  • Identities
  • Mathematics
  • Numbers
  • Orthogonality
  • Periodic Functions
  • Polynomials
  • Real Numbers
  • Sampling
  • Sequences
  • Standards
  • Theorems

Readers

  • Approximation Theory.