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Patterson-Sullivan distributions for symmetric spaces of the noncompact type
›
Preliminaries
›
Invariant differential operators
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
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Dissertation (PhD)
Patterson-Sullivan distributions for symmetric spaces of the noncompact type / Michael Schröder
Place and Date of Creation
2010
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