Tristan Leger: Spectral projectors and resolvent on the hyperbolic space
In this talk recent results on the Lp-Lq boundedness of spectral projectors and the resolvent operator on the real hyperbolic space will be discussed.
After giving some context, we will present a unified approach to both of these questions. We improve on existing results in the literature both by obtaining boundedness for a wider range of exponents (p; q), and by showing the sharp dependence of the implicit constant on the spectral parameter for projectors in the case of dual exponents.
Time permitting, applications to the Schrödinger equation on H^d and partial results on the boundedness of the extension operator will be presented.
This is joint work with Pierre Germain (Courant institute, NYU).
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