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

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• Alessio Martini (University of Birmingham)
• Thursday 02 October 2014, 16:00-17:00
• Physics 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 L^p 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 L^p-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.

This talk is included in these lists:

• Analysis seminar
• Physics West 117
• School of Mathematics events

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