Regularity of resonant states on a compact hyperbolic surface

Abstract

We will complete the calculation of Ruelle resonances of a compact hyperbolic surface, started in the last lecture, using the representation theory of PSL(2, R). The case of principal series will be treated in detail. We'll calculate the Fourier coefficients of resonant states and deduce that they belong to negative Sobolev spaces. This will be followed by a brief presentation of the theory of anisotropic Sobolev spaces, in order to compare the results obtained by the two methods (representation theory / anisotropic spaces).

Regularity of resonant states on a compact hyperbolic surface

Abstract

Speaker(s)

Nalini Anantharaman

Events

Graph and surface spectra (1)

Curves, Surfaces and Intersection

Regular graphs : Laplacian spectrum and geodesic flow correlation decay (1)

Prescribing the Spectra of Cubic Graphs

Regular graphs : Laplacian spectrum and decay of geodesic flow correlations (2)

Circuit QED Lattices: From Synthetic Quantum Systems to Spectral Graph The…

Laplacian spectrum and decay of geodesic flow correlations on hyperbolic surfaces (I)

Determinants of Laplacians and Random Surfaces

Laplacian spectrum and decay of geodesic flow correlations on hyperbolic surfaces (II)

Spectral projectors on hyperbolic surfaces

Regularity of resonant states on a compact hyperbolic surface

Poincaré Series and Convex Bodies on Flat Tori

Value in 0 of the Poincaré series of surfaces and graphs

Ruelle resonances for the geodesic flow on non-compact varieties

Optimal spectral hole for random regular graphs, after J. Friedman (I)

Low-Temperature Quantum Bounds on Curved Manifolds

Optimal spectral hole for random regular graphs, after J. Friedman (II)

From the geodesic flow to the wave equation on an Anosov variety

See also