Constructive Approximation and Harmonic Analysis

This research program focuses on the interaction between constructive approximation  and harmonic analysis. The aim is to facilitate broader and deeper interaction among researchers in these fields.

Approximation theory seeks to approximate complicated functions by simpler functions from certain classes and to evaluate the errors inevitably arising in such approximations. This field draws its methods from various areas of mathematics such as functional analysis, variational analysis, probability etc. Constructive approximation strives to explicitly find the best (or nearly best) approximants in such problems which is of tremendous importance in numerous applications.

Harmonic analysis is a very old branch of mathematics which investigates the behavior of functions using their time and frequency features as well as various (orthogonal) decompositions. Despite a long history, this field is very vital today with numerous open problems and active research areas, such as weighted inequalities, time-frequency analysis, multilineal analysis, singular integrals on rectifiable sets and many others. Harmonic analysis reveals exciting connections to other branches of mathematics, such as geometric measure theory, complex analysis, convex and discrete geometry.

Among all these relations, a very special place is taken by the link between harmonic analysis and approximation theory (this interplay is well known: trigonometric polynomials, wavelets, frames, other (quasi) orthogoAnal systems, hyperbolic cross approximations play an important role in approximation and are a subject of active ongoing research).​

Dmitriy Bilyk, University of Minnesota
Feng Dai, University of Alberta
Vladimir Temlyakov, University of South Carolina
Sergey Tikhonov, ICREA-CRM

Invited Researchers

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