"Orbital Integrals on Reductive Lie Groups and Their Algebras" by Francisco Bulnes

The purpose is to present a complete course on global analysis topics and establish some orbital applications of the integration on topological groups and their algebras to harmonic analysis and induced representations in representation theory.

Contents
Preface
1 Introduction
2 Integrals, Functional and Special Functions on Lie Groups and Lie Algebras
3 Orbital Integrals on Reductive Lie Groups
4 Orbital Integrals on Reductive Lie Algebras
5 Integral Transforms on Lie Groups and Lie Algebras
6 Intertwinning Operators
7 Some Examples of Orbital Integrals into Representation Theory on Field Theory and Integral Geometry
8 Orbital Integrals on Cuspidal Forms
9 Some Applications in the Study of Harmonic Analysis
10 Cohomological Induction and Securing of Generalized G-Modules by G(w)-Orbits to Infinite Dimensional Representations of Lie Groups
APPENDIX A: Integral Formulas on Canonical p-Pairs
APPENDIX B: Regularity on a Lie Algebra
APPENDIX C: Some Elements of the Asymptotic Behavior of the Matrix Coefficients
APPENDIX D: Coexeter Diagrams to some Integral Transforms in Representation Theory
APPENDIX E: Definition of a Real Reductive Group
Exercises
Technical Notation
Conclusion
References