Borel-Laplace Transform and Asymptotic Theory

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.

• 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.