Invariant projectors, dilation matrices, wavelets and multi-resolution analysis.

Pierre-Gilles Lemarié-Rieusset

Revista Matemática Iberoamericana (1994)

  • Volume: 10, Issue: 2, page 283-347
  • ISSN: 0213-2230

Abstract

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We show that (bi-orthogonal) wavelet bases associated to a dilation matrix which is compatible with integer shifts are generally provided by a multi-resolution analysis. The proof is done by studying the projectors which commute with integer shifts.

How to cite

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Lemarié-Rieusset, Pierre-Gilles. "Projecteurs invariants, matrices de dilatation, ondelettes et analyses multi-résolutions.." Revista Matemática Iberoamericana 10.2 (1994): 283-347. <http://eudml.org/doc/39452>.

@article{Lemarié1994,
author = {Lemarié-Rieusset, Pierre-Gilles},
journal = {Revista Matemática Iberoamericana},
keywords = {Proyecciones; Bases ortonormales; Ondículas; Traslaciones; Matrices de dilatación; dilation matrix; dilatation matrix; biorthogonality; almost- orthogonality; projector; Riesz type basis; basis of wavelets; multiresolution analysis},
language = {fre},
number = {2},
pages = {283-347},
title = {Projecteurs invariants, matrices de dilatation, ondelettes et analyses multi-résolutions.},
url = {http://eudml.org/doc/39452},
volume = {10},
year = {1994},
}

TY - JOUR
AU - Lemarié-Rieusset, Pierre-Gilles
TI - Projecteurs invariants, matrices de dilatation, ondelettes et analyses multi-résolutions.
JO - Revista Matemática Iberoamericana
PY - 1994
VL - 10
IS - 2
SP - 283
EP - 347
LA - fre
KW - Proyecciones; Bases ortonormales; Ondículas; Traslaciones; Matrices de dilatación; dilation matrix; dilatation matrix; biorthogonality; almost- orthogonality; projector; Riesz type basis; basis of wavelets; multiresolution analysis
UR - http://eudml.org/doc/39452
ER -

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