Quasianalytic Monogenic Solutions of a Cohomological Equation.

Intro -- Contents -- Chapter 1. Introduction -- Chapter 2. Monogenic Properties of the Solutions of the Cohomological Equation -- 2.1. C[sup(1)]-holomorphic and C#8734 -- -holomorphic functions -- 2.2. Borel's monogenic functions -- 2.3. Domains of monogenic regularity: The sequence (K[sub(j)]) -- 2.4. Monogenic regularity of the solutions -- 2.5. Whitney smoothness of monogenic functions -- Chapter 3. Carleman Classes at Diophantine Points -- 3.1. Carleman and Gevrey classes -- 3.2. Gevrey asymptotics at Diophantine points for monogenic functions -- 3.3. Borel transform at quadratic irrationals for the fundamental solution -- 3.4. Deduction of Theorem 3.4 from Theorem 3.5 -- 3.5. Proof of Theorem 3.5 -- Chapter 4. Resummation at Resonances and Constant-Type Points -- 4.1. Asymptotic expansions at resonances -- 4.2. Resurgence of the fundamental solution at resonances -- 4.3. Proof of Theorems 4.2 and 4.3 -- 4.4. A property of quasianalyticity at constant-type points -- Chapter 5. Conclusions and Applications -- 5.1. Gammel's series -- 5.2. An application to the problem of linearization of analytic diffeomorphisms of the circle -- 5.3. An application to a nonlinear small divisor problem (semi-standard map) -- Appendix -- A.l. Hadamard's product -- A.2. Some elementary properties of the fundamental solution -- A.3. Some arithmetical results. Continued fractions -- A.4. Proof of Lemma 3.3 -- A.5. Reminder about Borel-Laplace summation -- Bibliography.

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