Wavelets bases adapted to a self-similar quasicrystal
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
TypeArticle accepté pour publication ou publié
Journal nameJournal of Mathematical Physics
American Institute of Physics
MetadataShow full item record
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 / Keywordsquasicrystals; wavelet transforms; set theory
Showing items related by title and author.
Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations Mischler, Stéphane; Cañizo, José Alfredo; Caceres, Maria J. (2011) Article accepté pour publication ou publié
Cooling process for inelastic Boltzmann equations for hard spheres, Part II: Self-similar solutions and tail behavior Mouhot, Clément; Mischler, Stéphane (2006) Article accepté pour publication ou publié