Page 1

Displaying 1 – 9 of 9

Showing per page

Spaces with maximal projection constants

Hermann König, Nicole Tomczak-Jaegermann (2003)

Studia Mathematica

We show that n-dimensional spaces with maximal projection constants exist not only as subspaces of l but also as subspaces of l₁. They are characterized by a rigid set of vector conditions. Nevertheless, we show that, in general, there are many non-isometric spaces with maximal projection constants. Several examples are discussed in detail.

Sparse recovery with pre-Gaussian random matrices

Simon Foucart, Ming-Jun Lai (2010)

Studia Mathematica

For an m × N underdetermined system of linear equations with independent pre-Gaussian random coefficients satisfying simple moment conditions, it is proved that the s-sparse solutions of the system can be found by ℓ₁-minimization under the optimal condition m ≥ csln(eN/s). The main ingredient of the proof is a variation of a classical Restricted Isometry Property, where the inner norm becomes the ℓ₁-norm and the outer norm depends on probability distributions.

Stochastic approximation properties in Banach spaces

V. P. Fonf, W. B. Johnson, G. Pisier, D. Preiss (2003)

Studia Mathematica

We show that a Banach space X has the stochastic approximation property iff it has the stochasic basis property, and these properties are equivalent to the approximation property if X has nontrivial type. If for every Radon probability on X, there is an operator from an L p space into X whose range has probability one, then X is a quotient of an L p space. This extends a theorem of Sato’s which dealt with the case p = 2. In any infinite-dimensional Banach space X there is a compact set K so that for...

Sudakov-type minoration for log-concave vectors

Rafał Latała (2014)

Studia Mathematica

We formulate and discuss a conjecture concerning lower bounds for norms of log-concave vectors, which generalizes the classical Sudakov minoration principle for Gaussian vectors. We show that the conjecture holds for some special classes of log-concave measures and some weaker forms of it are satisfied in the general case. We also present some applications based on chaining techniques.

Currently displaying 1 – 9 of 9

Page 1