LEADER 03583nam 2200637 450 001 9910818014703321 005 20220422184946.0 010 $a1-4704-0378-1 035 $a(CKB)3360000000464964 035 $a(EBL)3114349 035 $a(SSID)ssj0000973838 035 $a(PQKBManifestationID)11630734 035 $a(PQKBTitleCode)TC0000973838 035 $a(PQKBWorkID)10988935 035 $a(PQKB)11209317 035 $a(MiAaPQ)EBC3114349 035 $a(RPAM)13127407 035 $a(PPN)19541666X 035 $a(EXLCZ)993360000000464964 100 $a20030318h20032003 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aQuasianalytic monogenic solutions of a cohomological equation /$fS. Marmi, D. Sauzin 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2003] 210 4$dİ2003 215 $a1 online resource (vi, 83 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 780 300 $a"Volume 164, number 780 (second of 5 numbers)." 311 $a0-8218-3325-1 0821833251 320 $aIncludes bibliographical references (pages 81-83). 327 $a""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Monogenic Properties of the Solutions of the Cohomological Equation""; ""A?2.1. C[sup(1)]a???holomorphic and C#8734; a???holomorphic functions""; ""A?2.2. Borel's monogenic functions""; ""A?2.3. Domains of monogenic regularity: The sequence (K[sub(j)])""; ""A?2.4. Monogenic regularity of the solutions""; ""A?2.5. Whitney smoothness of monogenic functions""; ""Chapter 3. Carleman Classes at Diophantine Points""; ""A?3.1. Carleman and Gevrey classes""; ""A?3.2. Gevrey asymptotics at Diophantine points for monogenic functions"" 327 $a""A?3.3. Borel transform at quadratic irrationals for the fundamental solution""""A?3.4. Deduction of Theorem 3.4 from Theorem 3.5""; ""A?3.5. Proof of Theorem 3.5""; ""Chapter 4. Resummation at Resonances and Constanta???Type Points""; ""A?4.1. Asymptotic expansions at resonances""; ""A?4.2. Resurgence of the fundamental solution at resonances""; ""A?4.3. Proof of Theorems 4.2 and 4.3""; ""A?4.4. A property of quasianalyticity at constanta???type points""; ""Chapter 5. Conclusions and Applications""; ""A?5.1. Gammel's series"" 327 $a""A?5.2. An application to the problem of linearization of analytic diffeomorphisms of the circle""""A?5.3. An application to a nonlinear small divisor problem (semia???standard map)""; ""Appendix""; ""A?A.l. Hadamard's product""; ""A?A.2. Some elementary properties of the fundamental solution""; ""A?A.3. Some arithmetical results. Continued fractions""; ""A?A.4. Proof of Lemma 3.3""; ""A?A.5. Reminder about Borela???Laplace summation""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 780. 606 $aMonogenic functions 606 $aSmall divisors 606 $aQuasianalytic functions 606 $aContinued fractions 615 0$aMonogenic functions. 615 0$aSmall divisors. 615 0$aQuasianalytic functions. 615 0$aContinued fractions. 676 $a510 s 676 $a515/.352 700 $aMarmi$b S$g(Stefano),$f1963-$042049 702 $aSauzin$b D.$f1966- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910818014703321 996 $aQuasianalytic monogenic solutions of a cohomological equation$94095804 997 $aUNINA