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Analyzable Functions and Applications
Edited by: O. Costin and M. D. Kruskal, Rutgers University, Piscataway, NJ, and A. Macintyre, University of London, UK
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Contemporary Mathematics
2005; 371 pp; softcover
Volume: 373
ISBN-10: 0-8218-3419-3
ISBN-13: 978-0-8218-3419-0
List Price: US$98
Member Price: US$78.40
Order Code: CONM/373
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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.

Readership

Graduate students and research mathematicians interested in asymptotic methods.

Table of Contents

  • S. Aït-Mokhtar -- A singularly perturbed Riccati equation
  • T. Aoki, T. Kawai, T. Koike, and Y. Takei -- On global aspects of exact WKB analysis of operators admitting infinitely many phases
  • M. Aschenbrenner and L. van den Dries -- Asymptotic differential algebra
  • W. Balser and V. Kostov -- Formally well-posed Cauchy problems for linear partial differential equations with constant coefficients
  • F. Blais, R. Moussu, and J.-P. Rolin -- Non-oscillating integral curves and o-minimal structures
  • B. Braaksma and R. Kuik -- Asymptotics and singularities for a class of difference equations
  • O. Costin -- Topological construction of transseries and introduction to generalized Borel summability
  • E. Delabaere -- Addendum to the hyperasymptotics for multidimensional Laplace integrals
  • F. Diener and M. Diener -- Higher-order terms for the de Moivre-Laplace theorem
  • J. Ecalle -- Twisted resurgence monomials and canonical-spherical synthesis of local objects
  • A. Fruchard and E. Matzinger -- Matching and singularities of canard values
  • B. Mudavanhu and R. E. O'Malley, Jr. -- On the renormalization method of Chen, Goldenfeld, and Oono
  • S. P. Norton -- Generalized surreal numbers
  • C. Olivé, D. Sauzin, and T. M. Seara -- Two examples of resurgence
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