Characterization of Sobolev-Slobodeckij spaces using geometric curvature energies

Characterization of Sobolev and BV Spaces

The main results of this paper are new characterizations of W (Ω), 1 < p < ∞, and BV (Ω) for Ω ⊂ R an arbitrary open set. Using these results, we answer some open questions of Brezis [11] and Ponce [32].

A new characterization of Sobolev spaces

Our main result is the following: Let g ∈ Lp(RN), 1 <p <+∞, be such that

Aggregation of SVM Classifiers Using Sobolev Spaces

This paper investigates statistical performances of Support Vector Machines (SVM) and considers the problem of adaptation to the margin parameter and to complexity. In particular we provide a classifier with no tuning parameter. It is a combination of SVM classifiers. Our contribution is two-fold: (1) we propose learning rates for SVM using Sobolev spaces and build a numerically realizable aggr...

Sobolev Spaces

Characterization of Smoothness of Multivariate Refinable Functions in Sobolev Spaces

Wavelets are generated from refinable functions by using multiresolution analysis. In this paper we investigate the smoothness properties of multivariate refinable functions in Sobolev spaces. We characterize the optimal smoothness of a multivariate refinable function in terms of the spectral radius of the corresponding transition operator restricted to a suitable finite dimensional invariant s...