Analyzable Functions and Applications
About this Title
O. Costin, M. D. Kruskal and A. Macintyre, Editors
The theory of analyzable functions is a technique used to study a wide class of asymptotic expansion methods and their applications in analysis, difference and differential equations, partial differential equations and other areas of mathematics.
Key ideas in the theory of analyzable functions were laid out by Euler, Cauchy, Stokes, Hardy, E. Borel, and others. Then in the early 1980s, this theory took a great leap forward with the work of J. Écalle. Similar techniques and concepts in analysis, logic, applied mathematics and surreal number theory emerged at essentially the same time and developed rapidly through the 1990s. The links among various approaches soon became apparent and this body of ideas is now recognized as a field of its own with numerous applications.
This volume stemmed from the International Workshop on Analyzable Functions and Applications held in Edinburgh (Scotland). The contributed articles, written by many leading experts, are suitable for graduate students and researchers interested in asymptotic methods.
Graduate students and research mathematicians interested in asymptotic methods.
Table of Contents
- Sadjia Aït-Mokhtar – A singularly perturbed Riccati equation [MR 2130823]
- Takashi Aoki, Takahiro Kawai, Tatsuya Koike and Yoshitsugu Takei – On global aspects of exact WKB analysis of operators admitting infinitely many phases [MR 2130824]
- Matthias Aschenbrenner and Lou van den Dries – Asymptotic differential algebra [MR 2130825]
- Werner Balser and Vladimir Kostov – Formally well-posed Cauchy problems for linear partial differential equations with constant coefficients [MR 2130826]
- F. Blais, R. Moussu and J.-P. Rolin – Non-oscillating integral curves and o-minimal structures [MR 2130827]
- Boele Braaksma and Robert Kuik – Asymptotics and singularities for a class of difference equations [MR 2130828]
- O. Costin – Topological construction of transseries and introduction to generalized Borel summability [MR 2130829]
- E. Delabaere – Addendum to the hyperasymptotics for multidimensional Laplace integrals [MR 2130830]
- Francine Diener and Marc Diener – Higher-order terms for the de Moivre-Laplace theorem [MR 2130831]
- Jean Ecalle – Twisted resurgence monomials and canonical-spherical synthesis of local objects [MR 2130832]
- A. Fruchard and E. Matzinger – Matching and singularities of canard values [MR 2130833]
- Blessing Mudavanhu and Robert E. O’Malley, Jr. – On the renormalization method of Chen, Goldenfeld, and Oono [MR 2130834]
- S. P. Norton – Generalizing surreal numbers [MR 2130835]
- C. Olivé, D. Sauzin and T. M. Seara – Two examples of resurgence [MR 2130836]