Marcinkiewicz-Zygmund Inequalities, Quadrature, and Approximation of Functions

30.01.2023 15:00 - 16:30

Frank Filbir (Helmholtz Center Munich & Technische Universität München)

In their seminal paper on trigonometric interpolation Jozef Marcinkiewicz and Antoni Zygmund [Mean values of trigonometrical polynomials, Fundamenta Mathematicae, 28 (1), 131-166, 1937] proved what is now called Marcinkiewicz-Zygmund inequalities (MZI) in relation to trigonometric interpolation. Later these inequalities had been generalized in many directions. MZI play a central role in various fields of applied mathematics such as approximation, sampling, quadrature, phase retrieval and many more. We will introduce the concept of MZI for deterministic scattered and random point configurations and will discuss consequences for approximation of functions on manifolds and on the q-dimensional unit sphere in particular. The talk is based on earlier work with Hrushikesh Mhaskar and on more recent work with Tino Ullrich, Ralf Hielscher, and Thomas Jahn.

L. Liehr and I. Shafkulovska
SR6 (1st floor)