Buch, Englisch, 288 Seiten, Format (B × H): 160 mm x 246 mm, Gewicht: 590 g
Introduction to Resurgent Analysis
Buch, Englisch, 288 Seiten, Format (B × H): 160 mm x 246 mm, Gewicht: 590 g
ISBN: 978-0-8493-9435-5
Verlag: Taylor & Francis Inc
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 precise, and the authors assume no previous knowledge of the subject. With this new book, mathematicians and other scientists can acquaint themselves with an interesting and powerful branch of asymptotic theory - the resurgent functions theory - and will learn techniques for applying it to solve problems in mathematics and mathematical sciences.
Zielgruppe
Professional
Autoren/Hrsg.
Weitere Infos & Material
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.
