Generalized wavelets and compactly supported scaling functions.

Pierre-Gilles Lemarié-Rieusset

Revista Matemática Iberoamericana (1993)

  • Volume: 9, Issue: 2, page 333-371
  • ISSN: 0213-2230

Abstract

top
We show that to any multi-resolution analysis of L2(R) with multiplicity d, dilation factor A (where A is an integer ≥ 2) and with compactly supported scaling functions we may associate compactly supported wavelets. Conversely, if (Ψε,j,k = Aj/2 Ψε (Ajx - k)), 1 ≤ ε ≤ E and j, k ∈ Z, is a Hilbertian basis of L2(R) with continuous compactly supported mother functions Ψε, then it is provided by a multi-resolution analysis with dilation factor A, multiplicity d = E / (A - 1) and with compactly supported scaling functions (which have the same regularity as the wavelets Ψε). Those results can be extended to the cases of exponentially localized functions and of biorthogonal wavelets.

How to cite

top

Lemarié-Rieusset, Pierre-Gilles. "Ondelettes generalisées et fonctions d'échelle à support compact.." Revista Matemática Iberoamericana 9.2 (1993): 333-371. <http://eudml.org/doc/39442>.

@article{Lemarié1993,
author = {Lemarié-Rieusset, Pierre-Gilles},
journal = {Revista Matemática Iberoamericana},
keywords = {Bases ortonormales; Ondículas; Bases de Hilbert; Localización; Proyecciones; translation invariant subspaces; biorthogonal basis; multiresolution analysis; dilation factor; wavelet basis; compactly supported wavelets; compactly supported scaling function},
language = {fre},
number = {2},
pages = {333-371},
title = {Ondelettes generalisées et fonctions d'échelle à support compact.},
url = {http://eudml.org/doc/39442},
volume = {9},
year = {1993},
}

TY - JOUR
AU - Lemarié-Rieusset, Pierre-Gilles
TI - Ondelettes generalisées et fonctions d'échelle à support compact.
JO - Revista Matemática Iberoamericana
PY - 1993
VL - 9
IS - 2
SP - 333
EP - 371
LA - fre
KW - Bases ortonormales; Ondículas; Bases de Hilbert; Localización; Proyecciones; translation invariant subspaces; biorthogonal basis; multiresolution analysis; dilation factor; wavelet basis; compactly supported wavelets; compactly supported scaling function
UR - http://eudml.org/doc/39442
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.