Original wavelets articles.

Question

I have spent most of the last two hours searching for the two original articles

• The article by Y. Meyer, where he constructs his smooth orthonormal wavelet basis for $L^2(\mathbb{R})$.

• The article by P. G. Lemarié-Rieusset, where he presents what will become known as the Battle-Lemarié wavelets.

I am aware that these articles probably is in French.

Are there any good detectives that might help?

Thanks :-)

Answer 1

The wavelet described in the wikipedia article on Meyer wavelet seems to be in his book Ondelettes et operateurs from 1990, which must be several years later than his first papers where he built it, but in that book it is reasonable that you will find a citation to the paper (and usually also a more easily digested format in books than in technical papers).

---

There seems to be an english translation "Wavelets and operators":

Meyer, Yves Wavelets and operators. Translated from the 1990 French original by D. H. Salinger. Cambridge Studies in Advanced Mathematics, 37. Cambridge University Press, Cambridge, 1992. xvi+224 pp. ISBN: 0-521-42000-8; 0-521-45869-2

Answer 2

I'm not sure about the first article. Here's an early article by Lemarié and Meyer, but there must be something even earlier. One sees references to

• Y. Meyer, La Transformation en Ondelettes et les Nouveaux Paraproduits, Actes du Colloque d'Analyse Nonlineaire du CEREMADE, Univ. Paris — Dauphine,

but I find no trace of the actual paper. There are also this, this, and this.

The second article you ask about may be

• P.G. Lemarié-Rieusset. Ondelettes à Localisation Exponentielle. J. Math. Pures Appl., 67 (1988), pp. 227–236.

Unfortunately, it doesn't appear to be online.