Hausdorff Colloquium

What are the compact sets in Lebesgue spaces?Hausdorff Colloquium

by Helge Holden (NTNU, Norway)

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Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Endenicher Allee 60/1-016 - Lipschitzsaal

Mathezentrum

90
Description

Abstract:

Compactness in Lebesgue spaces is fully characterized by the classical Kolomogorov–Riesz theorem.
We present how this theorem and the classical Arzelà–Ascoli theorem can be derived from a very elementary lemma. Furthermore, we show that one of the conditions of the Kolomogorov–Riesz theorem is redundant. 
Finally, we discuss how we can derive the Aubin–Lions–Dubinskii theorem  on compactness in Bochner spaces in this setting.

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Organized by

Barbara Verführt, Herbert Koch, Illia Karabaah