03583nam 2200637 450 991081801470332120220422184946.01-4704-0378-1(CKB)3360000000464964(EBL)3114349(SSID)ssj0000973838(PQKBManifestationID)11630734(PQKBTitleCode)TC0000973838(PQKBWorkID)10988935(PQKB)11209317(MiAaPQ)EBC3114349(RPAM)13127407(PPN)19541666X(EXLCZ)99336000000046496420030318h20032003 uy| 0engur|n|---|||||txtccrQuasianalytic monogenic solutions of a cohomological equation /S. Marmi, D. SauzinProvidence, Rhode Island :American Mathematical Society,[2003]©20031 online resource (vi, 83 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 780"Volume 164, number 780 (second of 5 numbers)."0-8218-3325-1 0821833251 Includes bibliographical references (pages 81-83).""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Monogenic Properties of the Solutions of the Cohomological Equation""; ""Â2.1. C[sup(1)]â€?holomorphic and C#8734; â€?holomorphic functions""; ""Â2.2. Borel's monogenic functions""; ""Â2.3. Domains of monogenic regularity: The sequence (K[sub(j)])""; ""Â2.4. Monogenic regularity of the solutions""; ""Â2.5. Whitney smoothness of monogenic functions""; ""Chapter 3. Carleman Classes at Diophantine Points""; ""Â3.1. Carleman and Gevrey classes""; ""Â3.2. Gevrey asymptotics at Diophantine points for monogenic functions""""Â3.3. Borel transform at quadratic irrationals for the fundamental solution""""Â3.4. Deduction of Theorem 3.4 from Theorem 3.5""; ""Â3.5. Proof of Theorem 3.5""; ""Chapter 4. Resummation at Resonances and Constantâ€?Type Points""; ""Â4.1. Asymptotic expansions at resonances""; ""Â4.2. Resurgence of the fundamental solution at resonances""; ""Â4.3. Proof of Theorems 4.2 and 4.3""; ""Â4.4. A property of quasianalyticity at constantâ€?type points""; ""Chapter 5. Conclusions and Applications""; ""Â5.1. Gammel's series""""Â5.2. An application to the problem of linearization of analytic diffeomorphisms of the circle""""Â5.3. An application to a nonlinear small divisor problem (semiâ€?standard map)""; ""Appendix""; ""ÂA.l. Hadamard's product""; ""ÂA.2. Some elementary properties of the fundamental solution""; ""ÂA.3. Some arithmetical results. Continued fractions""; ""ÂA.4. Proof of Lemma 3.3""; ""ÂA.5. Reminder about Borelâ€?Laplace summation""; ""Bibliography""Memoirs of the American Mathematical Society ;no. 780.Monogenic functionsSmall divisorsQuasianalytic functionsContinued fractionsMonogenic functions.Small divisors.Quasianalytic functions.Continued fractions.510 s515/.352Marmi S(Stefano),1963-42049Sauzin D.1966-MiAaPQMiAaPQMiAaPQBOOK9910818014703321Quasianalytic monogenic solutions of a cohomological equation4095804UNINA