Seminar: L2 Marcinkiewicz-Zygmund inequalities and frame subsampling

Time:

Venue/Location: Phòng C102, VIASM, 157 phố Chùa Láng, Hà Nội

Báo cáo viên: Felix Bartel, Chemnitz University of Technology, Germany

Abstract: The concept of Marcinkiewicz-Zygmund inequalities has been around since 1937 and was extensively studied by e.g. V. N. Temlyakov and coauthors. For a function space of finite dimension $m<\infty$ they establish a connection between the continuous $L_2$-norm to discrete function evaluations in points. Of special interest is the number of evaluations $n$ needed for this discretization. Naturally we need, $n\ge m$. In this lecture we show a construction achieving $n\sim m^2$ with optimal constants and a random construction such that $n\sim m\log m$. In order to achieve the optimal number of points, we make use of subsampling techniques which are related to the Kadison-Singer theorem. In this way we achieve a constructive way to obtain a subset of points fulfilling a $L_2$-Marcinkiewcz-Zygmund inequality such that $n\sim m$.