Wavelets bases adapted to a self-similar quasicrystal

Bernuau, Guillaume

Bernuau, Guillaume (1998), Wavelets bases adapted to a self-similar quasicrystal, Journal of Mathematical Physics, 39, p. n°4213. http://dx.doi.org/10.1063/1.532492

Type

Article accepté pour publication ou publié

Date

1998

Journal name

Journal of Mathematical Physics

Volume

Publisher

American Institute of Physics

Pages

n°4213

Abstract (EN)

Given any self-similar quasicrystal Λ in Rn with inflation θ>1, we construct bases of L2(Rn) having the following structure: θnj/2ψλ(θjx−λ), λ ∊ ΛθΛ, j ∊ Z, where the mother wavelets ψλ, λ ∊ ΛθΛ, are smooth and with exponential decay or compact support. We also show that wavelets ψλ constitute a relatively compact set in some Sobolev space and that they depend continuously on λ when Λ is equipped with an appropriate topology.

Subjects / Keywords

quasicrystals; wavelet transforms; set theory