This paper deals with the convergence of the wavelet thresholding estimator on Besov spaces B s p,q (R n ). We show firstly the equivalence of several Besov norms. It seems different with one dimensional case. Then we provide two convergence theorems for the wavelet thresholding estimator, which extend

The concept of R-duals was introduced by Casazza, Kutyniok, and Lammers in 2004. In this paper, we give a condition when a Parseval frame can be dilated to an orthonormal basis of a given separable Hilbert space H. This is advantageous for deriving a condition for a sequence {ω j } j∈J to be an R-dual of a given frame {f j } j∈J .

No abstract

A class of Besov spaces are characterized by the quadratic and cubic Hermite multiwavelets (K. Bittner and K. Urban, On interpolatory divergence-free wavelets, Math. Comp., 76 (2007), 903-929). That characterization has a limitation, because of the regularity restriction of the Hermite splines. In this paper, we extend Bittner and Urban's theorem by using Bspline wavelets with weak duals introduced in the paper: R. Q. Jia, J. Z. Wang and D. X. Zhou, Compactly supported wavelet bases for Sobolev spaces, Appl.

In this paper, we establish generalized sampling theorems, generalized stability theorems and new inequalities in the setting of shift-invariant subspaces of Lebesgue and Wiener amalgam spaces with mixed-norms. A convergence theorem of general iteration algorithms for sampling in some shift-invariant subspaces of Lp→(Rd) are also given.