Patterson-Sullivan distributions for symmetric spaces of the noncompact type / Michael Schröder. 2010
Inhalt
- Introduction
- Preliminaries
- Symmetric spaces and real semisimple Lie groups
- Geodesics, horocycles, and the boundary at infinity
- Invariant differential operators
- The classical examples
- Component computations
- Some integral formulas
- Derivatives corresponding to the Iwasawa decomposition
- Critical sets and Hessian forms
- Equivariant pseudodifferential operators on symmetric spaces
- Non-Euclidean Fourier analysis
- Invariance and equivariance properties
- Classes of symbols
- The Kohn-Nirenberg operator
- Conjugation by a wave group-type operator
- Helgason boundary values
- Poisson transform and principal series representations
- Regularity of distributional boundary values
- Tensor products of distributional boundary values
- Patterson-Sullivan distributions
- Intermediate values
- Definitions and invariance properties
- The Knapp-Stein intertwining operators
- An integral formula
- Eigenfunctions on a compact quotient
- The spectral order principle
- Bibliography
- Index