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Quantitative differentiation

Recent Developments in Harmonic Analysis May 15, 2017 - May 19, 2017

May 17, 2017 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Tuomas Hytönen (University of Helsinki)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • quantitative differentiation

  • embedding theorem

  • Sobolev space

  • harmonic analysis

  • partial differential equations

  • heat flow

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Hytönen

Abstract

As we learn in Calculus, differentiation is about approximating a given function by an affine one in infinitesimal balls. In quantitative differentiation, we would like to do the same in "macroscopic" balls of quantified size. There are now three approaches to the problem: "geometric", "analytic", and "dynamic". I will concentrate on the latter two, which I have considered in joint work with Assaf Naor (both) and Sean Li (the analytic approach). A key to both is a quantitative elaboration of Dorronsoro's classical embedding theorem of a Sobolev space into a certain local approximation space; in the "dynamic" version, this is achieved with the help of the heat flow.

Supplements
28690?type=thumb Hytonen Notes 470 KB application/pdf Download
Video/Audio Files

Hytönen

H.264 Video 10-Hytonen.mp4 251 MB video/mp4 rtsp://videos.msri.org/data/000/028/474/original/10-Hytonen.mp4 Download
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