Translational averaging for completeness, characterization and oversampling of wavelets.

Richard S. Laugesen

Collectanea Mathematica (2002)

  • Volume: 53, Issue: 3, page 211-249
  • ISSN: 0010-0757

Abstract

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The single underlying method of averaging the wavelet functional over translates yields first a new completeness criterion for orthonormal wavelet systems, and then a unified treatment of known results on characterization of wavelets on the Fourier transform side, on preservation of frame bounds by oversampling, and on equivalence of affine and quasiaffine frames. The method applies to multiwavelet systems in all dimensions, to dilation matrices that are in some cases not expanding, and to dual frame pairs.

How to cite

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Laugesen, Richard S.. "Translational averaging for completeness, characterization and oversampling of wavelets.." Collectanea Mathematica 53.3 (2002): 211-249. <http://eudml.org/doc/42924>.

@article{Laugesen2002,
abstract = {The single underlying method of averaging the wavelet functional over translates yields first a new completeness criterion for orthonormal wavelet systems, and then a unified treatment of known results on characterization of wavelets on the Fourier transform side, on preservation of frame bounds by oversampling, and on equivalence of affine and quasiaffine frames. The method applies to multiwavelet systems in all dimensions, to dilation matrices that are in some cases not expanding, and to dual frame pairs.},
author = {Laugesen, Richard S.},
journal = {Collectanea Mathematica},
keywords = {Ondículas; Completitud; Análisis de Fourier; Marcos de ondículas; Sobremuestreo; orthonormal wavelet; tight frame; oversampling; dual frame},
language = {eng},
number = {3},
pages = {211-249},
title = {Translational averaging for completeness, characterization and oversampling of wavelets.},
url = {http://eudml.org/doc/42924},
volume = {53},
year = {2002},
}

TY - JOUR
AU - Laugesen, Richard S.
TI - Translational averaging for completeness, characterization and oversampling of wavelets.
JO - Collectanea Mathematica
PY - 2002
VL - 53
IS - 3
SP - 211
EP - 249
AB - The single underlying method of averaging the wavelet functional over translates yields first a new completeness criterion for orthonormal wavelet systems, and then a unified treatment of known results on characterization of wavelets on the Fourier transform side, on preservation of frame bounds by oversampling, and on equivalence of affine and quasiaffine frames. The method applies to multiwavelet systems in all dimensions, to dilation matrices that are in some cases not expanding, and to dual frame pairs.
LA - eng
KW - Ondículas; Completitud; Análisis de Fourier; Marcos de ondículas; Sobremuestreo; orthonormal wavelet; tight frame; oversampling; dual frame
UR - http://eudml.org/doc/42924
ER -

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