Harmonic Analysis on Exponential Solvable Lie Groups

• ​1. Preliminaries: Lie groups and Lie algebras 2. Haar measure and group algebra 3. Induced representations 4. Four exponential solvable Lie groups 5. Orbit method 6. Kirillov Theory for nilpotent Lie groups 7. Holomorphically induced representations 8. Irreducible decomposition 9. e-central elements 10. Frobenius reciprocity 11. Plancherel formula 12. Commutativity conjecture: induction case 13. Commutativity conjecture: restriction case.

"The publication of this monograph is obviously an important event for experts in harmonic analysis and especially for researchers working in the theory of representations of solvable Lie groups. ... the appearance of this book is an important event which will strongly influence the development of the area." (Antoni Wawrzynczyk, Mathematical Reviews, October, 2015)