Frames and Stable Bases for Shift-Invariant Subspaces of L2(IRd)

Abstract

We study in this paper certain types of bases for shift-invariant subspaces. Our primary objective is to connect among three important families of basis sets: shift-invariant sets. Weyl-Heisenberg sets, and affine (wavelet) sets. The present paper is the first in a series of three, and is concerned with the basic theory of shift-invariant bases for the shift-invariant spaces. The two papers, (RS1) and (RS2), will focus on the applications of the theory developed here to Weyl-Heisenberg and affine sets

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1994
Accession Number
ADA276470

Entities

People

  • Amos Ron
  • Zuowei Shen

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Analogs
  • Conductive Polymers
  • Decomposition
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Filtration
  • Generators
  • Hilbert Space
  • Identities
  • Inequalities
  • Periodic Functions
  • Polynomials
  • Sequences
  • Theorems
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Image Processing and Computer Vision.
  • Linear Algebra

Technology Areas

  • Space