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Abstract: Recently, there was a big progress in studying sampling discretization of integral norms of functions from finite dimensional subspaces and from collections of such subspaces (universal discretization). It was established that sampling discretization results are useful in a number of applications. In particular, they turn out to be useful in sampling recovery. We will discuss some of those results.
The goal of this talk is to survey the corresponding results, and connect together ideas, methods, and results from different areas of research related to problems of discretization and recovery in the case of finite-dimensional subspaces.
Bio: Vladimir Temlyakov works in Steklov Mathematical Institute of RAS, Moscow State University, University of South Carolina. He is a top expert in function theory: approximations of functions in one variable and multivariable cases (approximations by polynomials, n-widths, optimal cubature formulas). Integral operators (estimates of singular numbers, approximation numbers, bilinear approximation of kernels of these operators).