Analyzable functions and applications : International Workshop on Analyzable Functions and Applications, June 17-21, 2002, International Centre for Mathematical Sciences, Edinburgh, Scotland / / O. Costin, M.D. Kruskal, A. Macintyre, editors

• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , [2005]; ©2005
• Descrizione fisica: 1 online resource (384 p.)
• Disciplina: 515
• Soggetto topico: Asymptotic expansions; Functions
• Soggetto genere / forma: Electronic books.
• Persona (resp. second.): CostinO <1960-> (Ovidiu); KruskalMartin D <1925-2006, > (Martin David); MacintyreA <1941-> (Angus)
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""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 examples""""2.1 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 transseries""""1.5. 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 theorem""""Twisted 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 monomials""""3. 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"" ; ""4.3 Semi-formal synthesis in Example 2""
• Titolo autorizzato: Analyzable functions and applications
• ISBN: 0-8218-7963-4; 0-8218-5707-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910480091403321
• Lo trovi qui: Univ. Federico II
• Serie: Contemporary mathematics (American Mathematical Society) ; ; v. 373.