Symplectic Methods in Harmonic Analysis and in Mathematical Physics

• Foreword.- Preface.- Prologue.- Part I: Symplectic Mechanics.- 1. Hamiltonian Mechanics in a Nutshell.- 2. The Symplectic Group.- 3. Free Symplectic Matrices.- 4. The Group of Hamiltonian Symplectomorphisms.- 5. Symplectic Capacities.- 6. Uncertainty Principles.- Part II: Harmonic Analysis in Symplectic Spaces.- 7. The Metaplectic Group.- 8. Heisenberg-Weyl and Grossmann-Royer Operators.- 9. Cross-ambiguity and Wigner Functions.- 10. The Weyl Correspondence.- 11. Coherent States and Anti-Wick Quantization.- 12. Hilbert-Schmidt and Trace Class Operators.- 13. Density Operator and Quantum States.- Part III: Pseudo-differential Operators and Function Spaces.- 14. Shubin's Global Operator Calculus.- Part IV: Applications.- 15. The Schrodinger Equation.- 16. The Feichtinger Algebra.- 17. The Modulation Spaces Mqs.- 18. Bopp Pseudo-differential Operators.- 19. Applications of Bopp Quantization.- Bibliography.- Index.

From the reviews: "The book under review presents new developments in harmonic analysis that have been inspired by research in quantum mechanics and time-frequency analysis. ... The book is well-written and the author has done a great job in organizing these diverse topics in a coherent manner. The presentation of the material makes it accessible to a graduate students in mathematics and physics, but researchers in harmonic analysis, quantum mechanics or time-frequency analysis will greatly benefit from the treatment of recent developments in these areas." (Franz Luef, Zentralblatt MATH, Vol. 1247, 2012) "This volume is based on a series of lectures on harmonic analysis on Rn and related subjects given by the author in Vienna in 2009; it contains 19 chapters, each of which (roughly) fits into a 90-minute lecture ... . covers also a number of topics not available elsewhere in book form, and moreover does that in a lively and readable fashion." (Miroslav Englis, Mathematical Reviews, Issue 2012 m)