1st Edition
Borel-Laplace Transform and Asymptotic Theory Introduction to Resurgent Analysis
288 Pages
by
CRC Press
The resurgent function theory introduced by J. Ecalle is one of the most interesting theories in mathematical analysis. In essence, the theory provides a resummation method for divergent power series (e.g., asymptotic series), and allows this method to be applied to mathematical problems. This new book introduces the methods and ideas inherent in resurgent analysis. The discussions are clear and... Read more
INTRODUCTION. Resurgent Analysis in the Theory of Differential Equations 0.1 Singular Points of Ordinary Differential Equations 0.2 Equations on Infinite Cylinder 0.3 Semi-classical Approximations CHAPTER 1. Borel-Laplace Transform 1.1 Entire Functions of Exponential Type 1.2 Hyperfunctions with Compact Support 1.3 Hyperfunctions of Exponential Growth 1.4 Microfunctions CHAPTER II. Resurgent Analysis 2.1 Preliminary Remarks 2.2 Resurgent Functions 2.3 Investigation Near Focal Points. Legendre Uniformization 2.4 Investigation Near Focal Points. Connection Homomorphism 2.5 Examples CHAPTER III. Applications 3.1 Ordinary Differential Equations 3.2 Partial Differential Equations 3.3 The Saddle Point Method APPENDIX. Integral Transforms of Ramifying Analytic Functions BIBLIOGRAPHY INDEX.
Biography
Boris Yu. Sternin, Professor of the Moscow State University, Doctor of Science in Physics and Mathematics, Moscow, Russia.
Victor E. Shatalov, Professor of the Moscow State University, Doctor of Science in Physics and Mathematics, Moscow, Russia.
