The purpose of this paper is to establish Lp error estimates, a Bernstein inequality, and inverse theorems for approximation by a space comprising spherical basis functions located at scattered sites on the unit n-sphere. In particular, the Bernstein inequality estimates Lp Bessel-potential Sobolev norms of functions in this space in terms of the minimal separation and the Lp norm of the functi...

The purpose of this paper is to establish Lp error estimates, a Bernstein inequality, and inverse theorems for approximation by a space comprising spherical basis functions located at scattered sites on the unit n-sphere. In particular, the Bernstein inequality estimates Lp Bessel-potential Sobolev norms of functions in this space in terms of the minimal separation and the Lp norm of the functi...

We consider best m-term approximation in Lp(R) with wave packets generated from a single refinable function. The main examples of such wave packets are orthonormal wavelets or more generally tight wavelet frames based on an MRA (so-called framelets). The approximation classes associated with best m-term approximation in Lp(R) with such wave packets are completely characterized in terms of Besov...

in this paper, we determine the structure of the space of multipliers of the range of a composition operator cφ that induces by the conditional expectation between two lp() spaces.

We consider best m-term approximation in Lp(R) with wave packets generated by a single refinable function. The main examples of wave packets are orthonormal wavelets, or more generally wavelet frames based on a multiresolution analysis (so-called framelets). The approximation classes associated with best m-term approximation in Lp(R) for a large class of wave packets are completely characterize...

We investigate the existence of infinite dimensional Banach spaces having rigid sets with an infinite number of elements. Among Banach lattices, examples are provided by infinite dimensional AM -spaces as well as for some abstract Lp-spaces, 1 ≤ p < ∞.