Book contents
- Frontmatter
- Dedication
- Contents
- Preface to the second edition
- Preface to the first edition
- List of Symbols
- Part I Combinatorial Enumeration
- Part II Mathematical Background
- 4 Fourier–Laplace integrals in one variable
- 5 Multivariate Fourier–Laplace integrals
- 6 Laurent series, amoebas, and convex geometry
- Part III Multivariate Enumeration
- Appendix A Integration on manifolds
- Appendix B Algebraic topology
- Appendix C Residue forms and classical Morse theory
- Appendix D Stratification and stratified Morse theory
- References
- Author Index
- Subject Index
5 - Multivariate Fourier–Laplace integrals
from Part II - Mathematical Background
Published online by Cambridge University Press: 08 February 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Preface to the second edition
- Preface to the first edition
- List of Symbols
- Part I Combinatorial Enumeration
- Part II Mathematical Background
- 4 Fourier–Laplace integrals in one variable
- 5 Multivariate Fourier–Laplace integrals
- 6 Laurent series, amoebas, and convex geometry
- Part III Multivariate Enumeration
- Appendix A Integration on manifolds
- Appendix B Algebraic topology
- Appendix C Residue forms and classical Morse theory
- Appendix D Stratification and stratified Morse theory
- References
- Author Index
- Subject Index
Summary
This chapter develops methods to compute asymptotics of multivariate Fourier–Laplace integrals in order to derive general saddle point approximations for use in later chapters. Our approach uses contour deformation, differing from common treatments relying on integration by parts: this requires analyticity rather than just smoothness but is better suited to integration over complex manifolds.
- Type
- Chapter
- Information
- Analytic Combinatorics in Several Variables , pp. 114 - 133Publisher: Cambridge University PressPrint publication year: 2024