05028nam 2200613 450 991078865970332120220825043720.00-8218-7963-40-8218-5707-X(CKB)3240000000069899(EBL)3113327(SSID)ssj0001034627(PQKBManifestationID)11592298(PQKBTitleCode)TC0001034627(PQKBWorkID)11017078(PQKB)10058176(MiAaPQ)EBC3113327(WaSeSS)Ind00039239(RPAM)13807513(PPN)197107001(EXLCZ)99324000000006989920041206h20052005 uy| 0engur|n|---|||||txtccrAnalyzable functions and applications International Workshop on Analyzable Functions and Applications, June 17-21, 2002, International Centre for Mathematical Sciences, Edinburgh, Scotland /O. Costin, Kruskal, A. Macintyre, editorsProvidence, Rhode Island :American Mathematical Society,[2005]©20051 online resource (384 p.)Contemporary mathematics,0271-4132 ;3730271-4132Description based upon print version of record.0-8218-3419-3 Includes bibliographical references.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.Contemporary mathematics (American Mathematical Society).3730271-4132Asymptotic expansionsCongressesFunctionsCongressesAsymptotic expansionsFunctions51531.49bclCostin O(Ovidiu),1960-Kruskal Martin D(Martin David),1925-2006,Macintyre A(Angus),1941-International Workshop on Analyzable Functions and ApplicationsMiAaPQMiAaPQMiAaPQBOOK9910788659703321Analyzable functions and applications3784923UNINA