We consider multilevel decompositions of piecewise constants on simplicial meshes that are stable in H − s ...

The main purpose of the present paper is to prove approximation and com-mutator properties for projections mapping periodic Sobolev spaces onto shift-invariant spaces generated by a nite number of compactly supported functions. With these prerequisites at hand and using certain localization techniques, we then characterize the stability of generalized Galerkin-Petrov schemes for solving periodi...

Many of the most common and useful properties of Sobolev spaces defined over a domain (open set) in Euclidean space require that the domain has a minimal degree of regularity. To this end, the domain is often assumed to satisfy a “cone condition.” For example, various imbeddings of Sobolev spaces into Lebesgue spaces or spaces of bounded continuous functions (the Sobolev imbedding theorem), and...

Olshausen and Field (1996) applied the principle of independence maximization by sparse coding to extract features from natural images. This leads to the emergence of oriented linear filters that have simultaneous localization in space and in frequency, thus resembling Gabor functions and simple cell receptive fields. In this article, we show that the same principle of independence maximization...

A unified approach to embedding theorems for Sobolev type spaces of vector-valued functions, defined via their symmetric gradient, is proposed. The in question are built upon general rearrangement-invariant norms. Optimal target the relevant embeddings determined within class all spaces. In particular, gradient into shown be equivalent corresponding full same sharp condition uniformly continuou...