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Seminario de Analisis y Aplicaciones 15_02

Dpto. de Matemáticas
Javier Parcet ICMAT
Módulo 17 - Aula 520 (Dpto. Matemáticas UAM)

Resumen: In harmonic analysis terms, Lafforgue/de la Salle rigidity theorem for SLn(R)
implies that Fourier summability fails in Lp when p is large enough in terms of
the rank n 􀀀 1. It refines older celebrated results by Harish-Chandra, Cowling
or Haagerup, and spotlights the dramatic difference between abelian and
semisimple harmonic analysis.

We shall present the first sufficient condition for Lp-boundedness of Fourier multipliers in this context, which is reminiscent of the H¨ ormander-Mikhlin criterion, but substantially and necessarily different to accommodate rigidity. Next, we shall introduce a major strengthening of the rigidity theorem and link it with Bochner-Riesz summability problems. Emphasis will be put on the harmonic analysis aspects of both of these results. Joint work with ´Eric Ricard and Mikael de la Salle.

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