Spectra of higher rank locally symmetric spaces / von Lasse Lennart Wolf ; unter der Betreuung durch Prof. Dr. Tobias Weich. Paderborn, 2023
Inhalt
- Abstract
- Zusammenfassung
- Danksagung
- Preface
- Introduction
- Ruelle resonances
- Laplace spectrum
- Quantum-classical correspondence
- Locally symmetric spaces
- Quantum and classical operators
- Summary of the publications
- Preliminaries
- Bibliography
- Projects
- Quantum-classical correspondence
- Published Paper
- Introduction
- Preliminaries
- Ruelle-Taylor resonances for higher rank Anosov actions
- Semisimple Lie groups
- Principal series representations
- Invariant differential operators
- Poisson transform
- L^p bounds for elementary spherical functions
- Positive definite functions and unitary representations
- Associated vector bundles
- Ruelle-Taylor resonances for the Weyl chamber action
- Lifted Weyl chamber action
- First band resonances and horocycle operators
- First band resonant states and principal series representation
- Quantum-classical correspondence
- Quantum spectrum
- Main Theorem
- Supplementary Material
- Bibliography
- Absence of principal eigenvalues
- Preliminary Material
- Published Paper
- Introduction
- Preliminaries
- Symmetric spaces
- Invariant differential operators
- Geodesic compactification
- Maximal Satake compactification
- Moderate growth
- Absence of imaginary values in the L^2 spectrum
- Examples
- Bibliography
- Temperedness of local product symmetric spaces
- Published Paper
- Introduction
- Preliminaries
- Setting
- Spherical functions
- Functions of positive type and unitary representations
- Harish-Chandra's c-Function
- The Fourier-Helgason transform
- Spectra for locally symmetric spaces
- The spectrum for quotients of products of rank one space
- Bibliography