Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605543 | Applied and Computational Harmonic Analysis | 2008 | 7 Pages |
Abstract
Assume ÏâL2(Rd) has Fourier transform continuous at the origin, with ÏË(0)=1, and that âlâZd|ÏË(ξâl)|2 is bounded as a function of ξâRd. Then every function fâL2(Rd) can be represented by an affine series f=âj>0âkâZdcj,kÏj,k for some coefficients satisfyingâcââ1(â2)=âj>0(âkâZd|cj,k|2)1/2<â. Here Ïj,k(x)=|detaj|1/2Ï(ajxâk) and the dilation matrices aj expand, for example aj=2jI. The result improves an observation by Daubechies that the linear combinations of the Ïj,k are dense in L2(Rd).
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
H.-Q. Bui, N. Kaiblinger, R.S. Laugesen,