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Analyzable Functions and Applications
 
Edited by: O. Costin Rutgers University, Piscataway, NJ
M. D. Kruskal Rutgers University, Piscataway, NJ
A. Macintyre University of London, London, UK
Analyzable Functions and Applications
Softcover ISBN:  978-0-8218-3419-0
Product Code:  CONM/373
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7963-4
Product Code:  CONM/373.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-3419-0
eBook: ISBN:  978-0-8218-7963-4
Product Code:  CONM/373.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Analyzable Functions and Applications
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Analyzable Functions and Applications
Edited by: O. Costin Rutgers University, Piscataway, NJ
M. D. Kruskal Rutgers University, Piscataway, NJ
A. Macintyre University of London, London, UK
Softcover ISBN:  978-0-8218-3419-0
Product Code:  CONM/373
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7963-4
Product Code:  CONM/373.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-3419-0
eBook ISBN:  978-0-8218-7963-4
Product Code:  CONM/373.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 3732005; 371 pp
    MSC: Primary 03; 34; 58; 40; 39;

    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
     
     
    • Articles
    • 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 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 3732005; 371 pp
MSC: Primary 03; 34; 58; 40; 39;

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.

  • Articles
  • 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 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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