The problem is discussed of replacing an integral norm with respect to a given probability
measure by the corresponding integral norm with respect to a discrete measure. This …

It is well known that there is a mathematical equivalence between 'solving'parabolic partial
differential equations (PDEs) and 'the integration'of certain functionals on Wiener space …

This survey is mainly intended for non-specialists, though we try to include many recent
developments that may interest the experts as well. We want to study “good” finite subsets of …

Let β≡ β (2n) be an N-dimensional real multi-sequence of degree 2n, with associated
moment matrix 𝓜 (n)≡ 𝓜 (n)(β), and let r:= rank 𝓜 (n). We prove that if 𝓜 (n) is positive …

We provide a simple proof of Tchakaloff's Theorem on the existence of cubature formulas of
degree $ m $ for Borel measures with moments up to order $ m $. The result improves …

Flat Extensions of Positive Moment Matrices: Recursively Generated Relations Raúl E. Curto
Lawrence A. Fialkow Page 1 Flat Extensions of Positive Moment Matrices: Recursively Generated …

The generalized problem of moments is a conic linear optimization problem over the convex
cone of positive Borel measures with given support. It has a large variety of applications …

We introduce an efficient algorithm for computing Carathéodory cubature measures, which
are defined as interpolatory cubature measures with positive weights, whose cardinality …

This expository essay discusses a finite dimensional approach to dilation theory. How much
of dilation theory can be worked out within the realm of linear algebra? It turns out that some …

Let [Formula: see text] denote a d-dimensional real multisequence, let K denote a closed
subset of Rd, and let P2n:={p∈ R [x1,…, xd]: degp⩽ 2n}. Corresponding to β, the Riesz …