Analyzable Functions and Applications.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Costin, O.
Otros Autores: Kruskal, M. D., Macintyre, A.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 2005.
Colección:Contemporary Mathematics.
Temas:
Asymptotic expansions > Congresses.
Functions > Congresses.
Développements asymptotiques > Congrès.
Fonctions (Mathématiques) > Congrès.
Asymptotic expansions
Functions
Conference papers and proceedings
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Contents
  • Preface
  • A singularly perturbed Riccati equation
  • On global aspects of exact WKB analysis of operators admitting infinitely many phases
  • Asymptotic differential algebra
  • Introduction
  • 1. Hardy Fields
  • 2. The Field of Logarithmic-Exponential Series
  • 3. H-Fields and Asymptotic Couples
  • 4. Algebraic Differential Equations over H-Fields
  • References
  • Formally well-posed Cauchy problems for linear partial differential equations with constant coefficients
  • Non-oscillating integral curves and O-minimal structures
  • 1. Introduction
  • 2. Definitions and examples2.1 Hardy fields and o-minimal structures
  • 2.2 Boshernitzan's example
  • 2.3 Quasianalytic Denjoy-Carleman classes
  • 3. Euler's equation
  • 3.1 Euler's equation in the real plane
  • 3.2 Euler's equation in the complex plane
  • 3.3 Formal conjugation
  • Asymptotics and singularities for a class of difference equations
  • Topological construction of transseries and introduction to generalized Borel summability
  • 1. Introduction
  • 1.1. Abstract multiseries
  • 1.2. Topology on multiseries
  • 1.3. Contractive operators
  • 1.4. Inductive construction of logarithm-free transseries1.5. The space T of general transseries
  • 2. Equations in T: examples
  • 2.1. Multidimensional systems: transseries solutions at irregular singularities of rank one
  • 3. Borel summation techniques
  • 3.1. Borel summation of transseries: a first order example
  • 3.2. Generalized Borel summation for rank one ODEs
  • 3.3. Difference equations and PDEs
  • 3.4. More general irregular singularities and multisummability
  • References
  • Addendum to the hyperasymptotics for multidimensional Laplace integrals
  • Higher-order terms for the de Moivre-Laplace theoremTwisted resurgence monomials and canonical-spherical synthesis of local objects
  • 1. Introduction: Object Analysis and Object Synthesis
  • 1.1 The notion of Local Analytic Object
  • 1.2 Object Analysis: the Bridge Equation
  • 1.3 Object Synthesis: semi-formal candidates
  • 1.4 Object Synthesis: from semi-formal to effective
  • 2. Reminders about moulds, resurgent functions, alien derivations
  • 2.1 Moulds/comoulds
  • 2.2 Resurgent functions
  • 2.3 Alien derivations or automorphisms. Their weights
  • 2.4 Resurgence monomials3. Object Analysis: six basic examples
  • 3.1 Example 1: shift-like diffeomorphism
  • 3.2 Example 2: Euler-like differential equation
  • 3.3 Example 3: monocritical linear differential system
  • 3.4 Example 4: monocritical non-linear differential system
  • 3.5 Example 5: polycritical linear differential system
  • 3.6 Example 6: polycritical non-linear differential system
  • 4. The reverse problem: Object Synthesis
  • 4.1 Standard or hyperlogarithmic resurgence monomials and monics
  • 4.2 Semi-formal synthesis in Example 1

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