# Mathematical Scattering Theory: Analytic Theory

### About this Title

**D. R. Yafaev**, *Université Rennes 1, Rennes, France*

Publication: Mathematical Surveys and Monographs

Publication Year:
2010; Volume 158

ISBNs: 978-0-8218-0331-8 (print); 978-1-4704-1385-9 (online)

DOI: https://doi.org/http://dx.doi.org/10.1090/surv/158

MathSciNet review: MR2598115

MSC: Primary 47A40; Secondary 34L25, 35-02, 35P25, 47E05, 81U05

### Table of Contents

**Front/Back Matter**

**Chapters**

- 1. Basic notation
- 2. Introduction
- 3. Basic concepts
- 4. Smooth theory. The Schrödinger operator
- 5. Smooth theory. General differential operators
- 6. Scattering for perturbations of trace class type
- 7. Scattering on the half-line
- 8. One-dimensional scattering
- 9. The limiting absorption principle (LAP), the radiation conditions and the expansion theorem
- 10. High- and lower-energy asymptotics
- 11. The scattering matrix (SM) and the scattering cross section
- 12. The spectral shift function and trace formulas
- 13. The Schrödinger operator with a long-range potential
- 14. The LAP and radiation estimates revisited
- 15. Review of the literature