University of Birmingham > Talks@bham > Analysis seminar > Spectral multipliers and wave equation for sub-Laplacians

## Spectral multipliers and wave equation for sub-LaplaciansAdd to your list(s) Download to your calendar using vCal - Sebastiano Nicolussi Golo (University of Birmingham)
- Wednesday 14 November 2018, 09:30-10:30
- Poynting Small Lecture Theatre (S06).
If you have a question about this talk, please contact Diogo Oliveira E Silva. Mihlin-Hörmander theorem gives the sharp Sobolev order n/2 for a spectral multiplier of the Laplacian to define a bounded operator on L^p for all p∈(1,∞). We study the same type of statements for sub-Laplacians, which are sub-elliptic operators defined on sub-Riemannian manifolds. It is known that the homogeneous dimension Q can play the same role as n on certain sub-Riemannian manifolds. However, there are examples, such as the Heisenberg groups, where Q>n but n/2 is again the sharp Sobolev order. Here, n is the topological dimension. These results led to conjecture that the sharp Sobolev order for a Mihlin-Hörmander theorem is half the topological dimension in a large class of sub-Riemannian manifolds, e.g., Carnot groups. We have proven that in no sub-Riemannian manifold the sharp Sobolev order can be lower than half the topological dimension. For the proof, we construct a partial Fourier integral representation of the sub-Riemannian wave propagator. This is a joint work with Alessio Martini and Detlef Müller. This talk is part of the Analysis seminar series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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