Title
PattersonSullivan distributions for symmetric spaces: PattersonSullivan distributions for symmetric spaces of the noncompact t,Used
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In his dissertation written at the University of Paderborn under the supervision of Prof. Dr. Joachim Hilgert, the author generalizes parts of a special nonEuclidean calculus of pseudodifferential operators, which was invented by S. Zelditch for hyperbolic surfaces, to symmetric spaces X=G/K of the noncompact type and their compact quotients spaces of nonpositive sectional curvature. Some results are restricted to the case of rank one symmetric spcaes. The nonEuclidean setting extends the defintion of socalled PattersonSullivan distributions, which were first defined by N. Anantharaman and S. Zelditch for hyperbolic systems, in a natural way to arbitrary symmetric spaces of the noncompact type. The author finds an explicit intertwining operator mapping PattersonSullivan distributions into Wigner distributions, he studies the important invariance and equivariance properties of these distributions and finally, he describes asymptotic properties of these distributions. Further research, results and generalizations will appear elsewhere in the future as a joint work together with J. Hilgert and S. Hansen.
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