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200 10$aQuasianalytic monogenic solutions of a cohomological equation /$fS. Marmi, D. Sauzin
210  1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2003]
210  4$d©2003
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
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