Given a Banach space X and one of its compact sets F , we consider the problem of finding a good n dimensional space Xn âŠ‚ X which can be used to approximate the elements of F . The best possibleâ€¦ (More)

In compressed sensing we seek to gain information about vector x âˆˆ R from d << N nonadaptive linear measurements. Candes, Donoho, Tao et. al. ( see e.g. [2, 4, 8]) proposed to seek good approximationâ€¦ (More)

The study of how to fuse measurement data with parametric models for PDEs has led to a new spectrum of problems in optimal recovery. A classical setting of optimal recovery is that one has a boundedâ€¦ (More)

We discuss known results (c.f. [16, 6]) about stability of `1 minimisation (denoted âˆ†1) with respect to the measurement error and how those results depend on the measurement matrix Î¦. Then we produceâ€¦ (More)

Compressed sensing aims at recovering a sparse signal x âˆˆ RN from few nonadaptive, linear measurements Î¦(x) given by a measurement matrix Î¦. One of the fundamental recovery algorithms is an `1â€¦ (More)

We are interested in the question when a Banach space X with an unconditional basis is isomorphic (as a Banach space) to an order-continuous nonatomic Banach lattice. We show that this is the case ifâ€¦ (More)