LEADER 05028nam 2200613 450 001 9910788659703321 005 20220825043720.0 010 $a0-8218-7963-4 010 $a0-8218-5707-X 035 $a(CKB)3240000000069899 035 $a(EBL)3113327 035 $a(SSID)ssj0001034627 035 $a(PQKBManifestationID)11592298 035 $a(PQKBTitleCode)TC0001034627 035 $a(PQKBWorkID)11017078 035 $a(PQKB)10058176 035 $a(MiAaPQ)EBC3113327 035 $a(WaSeSS)Ind00039239 035 $a(RPAM)13807513 035 $a(PPN)197107001 035 $a(EXLCZ)993240000000069899 100 $a20041206h20052005 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnalyzable functions and applications $eInternational Workshop on Analyzable Functions and Applications, June 17-21, 2002, International Centre for Mathematical Sciences, Edinburgh, Scotland /$fO. Costin, Kruskal, A. Macintyre, editors 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2005] 210 4$dİ2005 215 $a1 online resource (384 p.) 225 1 $aContemporary mathematics,$x0271-4132 ;$v373$x0271-4132 300 $aDescription based upon print version of record. 311 $a0-8218-3419-3 320 $aIncludes bibliographical references. 327 $aContents -- 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. 410 0$aContemporary mathematics (American Mathematical Society).$v373$x0271-4132 606 $aAsymptotic expansions$vCongresses 606 $aFunctions$vCongresses 615 0$aAsymptotic expansions 615 0$aFunctions 676 $a515 686 $a31.49$2bcl 702 $aCostin$b O$g(Ovidiu),$f1960- 702 $aKruskal$b Martin D$g(Martin David),$f1925-2006, 702 $aMacintyre$b A$g(Angus),$f1941- 712 12$aInternational Workshop on Analyzable Functions and Applications 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788659703321 996 $aAnalyzable functions and applications$93784923 997 $aUNINA