Analyzable Functions and Applications

Analyzable Functions and Applications

by O. Costin, A. MacIntyre
     
 

ISBN-10: 0821834193

ISBN-13: 9780821834190

Pub. Date: 04/01/2005

Publisher: American Mathematical Society

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.

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Overview

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. Ecalle. 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.

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Product Details

ISBN-13:
9780821834190
Publisher:
American Mathematical Society
Publication date:
04/01/2005
Series:
Contemporary Mathematics Series, #373
Pages:
371
Product dimensions:
70.00(w) x 97.50(h) x 7.50(d)

Table of Contents

A singularly perturbed Riccati equation1
On global aspects of exact WKB analysis of operators admitting infinitely many phases11
Asymptotic differential algebra49
Formally well-posed Cauchy problems for linear partial differential equations with constant coefficients87
Non-oscillating integral curves and o-minimal structures103
Asymptotics and singularities for a class of difference equations113
Topological construction of transseries and introduction to generalized Borel summability137
Addendum to the hyperasymptotics for multidimensional Laplace integrals177
Higher-order terms for the de Moivre-Laplace theorem191
Twisted resurgence monomials and canonical-spherical synthesis of local objects207
Matching and singularities of canard values317
On the renormalization method of Chen, Goldenfeld, and Oono337
Generalizing surreal numbers347
Two examples of resurgence355

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