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Seminario: Spectral multipliers for the Kohn Laplacian on complex spheres

Mercoledì 17 Dicembre 2014, ore 12:30 - Aula 2BC30 - Alessio Martini

ARGOMENTI: Seminari

Mercoledì 17 Dicembre 2014 alle ore 12:30 in aula 2BC30 il Dott. Alessio Martini (Università di Birmingham) terrà un seminario dal titolo "Spectral multipliers for the Kohn Laplacian on complex spheres".

Abstract
The Kohn Laplacian L associated to the tangential Cauchy-Riemann complex on a strongly pseudoconvex CR manifold M is a classic example of a non-elliptic, hypoelliptic differential operator. In the case M is the unit sphere in C^n, a great amount of information about the spectral theory of L can be obtained via representation theory of unitary groups. Following this approach, in joint work with V. Casarino (Padova), M. Cowling (Sydney), and A. Sikora (Sydney), we prove a multiplier theorem of Mihlin--Hoermander type for L that improves previously known results. It is still an open question whether the same improvement can be obtained for an arbitrary compact strongly pseudoconvex CR manifold M.

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