Ondelettes generalisées et fonctions d'échelle à support compact

Autores: Pierre Gilles Lemarié-Rieusset
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 9, Nº 2, 1993, págs. 333-372
Idioma: francés
DOI: 10.4171/rmi/140
Títulos paralelos:
- Ondículas generalizadas y funciones de escala con soporte compacto.
- Generalized wavelets and compactly supported scaling functions.
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Resumen
- 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 (?e,j,k = Aj/2 ?e (Ajx - k)), 1 = e = E and j, k Î Z, is a Hilbertian basis of L2(R) with continuous compactly supported mother functions ?e, 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 ?e). Those results can be extended to the cases of exponentially localized functions and of biorthogonal wavelets.