Traces of Oscillating Functions.
Tractable embeddings of Besov spaces into Zygmund spaces
The paper deals with dimension-controllable (tractable) embeddings of Besov spaces on n-dimensional cubes into Zygmund spaces. This can be expressed in terms of tractability envelopes.
Transformée en paquets d'ondelettes des signaux stationnaires: comportement asymptotique des densités spectrales.
We consider quadrature mirror filters, and the associated wavelet packet transform. Let X = {Xn}n∈Z be a stationary signal which has a continuous spectral density f. We prove that the 2n signals obtained from X by n iterations of the transform converge to white noises when n → +∞. If f is holderian, the convergence rate is exponential.
Translational averaging for completeness, characterization and oversampling of wavelets.
The single underlying method of averaging the wavelet functional over translates yields first a new completeness criterion for orthonormal wavelet systems, and then a unified treatment of known results on characterization of wavelets on the Fourier transform side, on preservation of frame bounds by oversampling, and on equivalence of affine and quasiaffine frames. The method applies to multiwavelet systems in all dimensions, to dilation matrices that are in some cases not expanding, and to dual...
Two-dimensional Legendre wavelets and operational matrices of integration.
Two-microlocal Besov spaces and wavelets