Record Nr.

UNINA9910788849903321

Autore

Marmi S (Stefano), <1963->

Titolo

Quasianalytic monogenic solutions of a cohomological equation / / S. Marmi, D. Sauzin

Pubbl/distr/stampa


Providence, Rhode Island : , : American Mathematical Society, , [2003]
©2003

ISBN

1-4704-0378-1

Descrizione fisica

1 online resource (vi, 83 p.)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 780

Disciplina

510 s

515/.352

Soggetti

Monogenic functions

Small divisors

Quasianalytic functions

Continued fractions

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"Volume 164, number 780 (second of 5 numbers)."

Nota di bibliografia

Includes bibliographical references (pages 81-83).

Nota di contenuto

""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""