University of Birmingham > Talks@bham > Analysis Seminar > Spectral multipliers and group representations: analysis of the Kohn Laplacian on complex spheres

Spectral multipliers and group representations: analysis of the Kohn Laplacian on complex spheres

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  • UserAlessio Martini (University of Birmingham)
  • ClockThursday 02 October 2014, 16:00-17:00
  • HousePhysics West 117.

If you have a question about this talk, please contact José Cañizo.

This is a joint Algebra-Analysis seminar

Let L be the Laplacian on Rn. The investigation of necessary and sufficient conditions for an operator of the form F(L) to be bounded on Lp in terms of “smoothness properties” of the spectral multiplier F is a classical research area of harmonic analysis, with long-standing open problems (e.g., the Bochner-Riesz conjecture) and connections with the regularity theory of PDEs.

In settings other than the Euclidean, particularly in the presence of a sub-Riemannian geometric structure, the natural substitute L for the Laplacian need not be an elliptic operator, and it may be just hypoelliptic. In this context, even the simplest questions related to the Lp-boundedness of operators of the form F(L) are far from being completely understood.

I will present some recent result, obtained in joint work with V. Casarino (Padova), M. Cowling (Sydney), and A. Sikora (Sydney), in the case where L is the Kohn Laplacian acting on forms on complex spheres. Due to the symmetries of the Kohn Laplacian L, the representation theory of the unitary group U(n) plays a prominent role in our analysis.

This talk is part of the Analysis Seminar series.

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