Lectures on the Kato square root problem

Details Lectures on the Kato square root problem Lectures on the Kato square root problem

2001-08-04

arxiv.org/abs/math/0108029v1

Mathematics

Classical Analysis and ODEs

For those who want some explanations about the proof without too much details

Scientific paper

This is the text of a series of three lectures given at the CMA of the Australian National University on the recent solution of the square root problem for divergence form elliptic operators, a long-standing conjecture posed by Kato in the early 60's. In this text, the motivations for this problem and its situation are given. The ideas from harmonic analysis on the T(1) theorem and T(b) theorem for square functions are described. In particular, an apparently new formulation of a local T(b) theorem for square functions is stated. The ideas of the full proof are presented. I want to thank the CMA at the Australian National University for inviting me during the special program on scattering theory and spectral problems and for the nice and stimulating atmosphere created by the mathematicians at the CMA.

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