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Quasianalytic monogenic solutions of a cohomological equation / / S. Marmi, D. Sauzin
| Quasianalytic monogenic solutions of a cohomological equation / / S. Marmi, D. Sauzin |
| Autore | Marmi S (Stefano), <1963-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2003] |
| Descrizione fisica | 1 online resource (98 p.) |
| Disciplina |
510 s
515/.352 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Monogenic functions
Small divisors Quasianalytic functions Continued fractions |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0378-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910480010103321 |
Marmi S (Stefano), <1963->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2003] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Quasianalytic monogenic solutions of a cohomological equation / / S. Marmi, D. Sauzin
| Quasianalytic monogenic solutions of a cohomological equation / / S. Marmi, D. Sauzin |
| Autore | Marmi S (Stefano), <1963-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2003] |
| Descrizione fisica | 1 online resource (vi, 83 p.) |
| Disciplina |
510 s
515/.352 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Monogenic functions
Small divisors Quasianalytic functions Continued fractions |
| ISBN | 1-4704-0378-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910788849903321 |
|
Marmi S (Stefano), <1963->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2003] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Quasianalytic monogenic solutions of a cohomological equation / / S. Marmi, D. Sauzin
| Quasianalytic monogenic solutions of a cohomological equation / / S. Marmi, D. Sauzin |
| Autore | Marmi S (Stefano), <1963-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2003] |
| Descrizione fisica | 1 online resource (vi, 83 p.) |
| Disciplina |
510 s
515/.352 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Monogenic functions
Small divisors Quasianalytic functions Continued fractions |
| ISBN | 1-4704-0378-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910818014703321 |
|
Marmi S (Stefano), <1963->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2003] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Small divisor problem in the theory of three-dimensional water gravity waves / / Gérard Iooss, Pavel I. Plotnikov
| Small divisor problem in the theory of three-dimensional water gravity waves / / Gérard Iooss, Pavel I. Plotnikov |
| Autore | Iooss Gérard |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (144 p.) |
| Disciplina | 532.593 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Water waves
Gravity waves Multiphase flow - Mathematical models Pseudodifferential operators Boundary value problems Bifurcation theory Small divisors |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0554-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""3.3. Main orders of the diffeomorphism and coefficient v""""Chapter 4. Small Divisors. Estimate of L � Resolvent""; ""4.1. Proof of Theorem 4.10""; ""Chapter 5. Descent Method-Inversion of the Linearized Operator""; ""5.1. Descent method""; ""5.2. Proof of Theorem 5.1""; ""5.3. Verification of assumptions of Theorem 5.1""; ""5.4. Inversion of L""; ""Chapter 6. Nonlinear Problem. Proof of Theorem 1.3""; ""Appendix A. Analytical study of G[sub(n)]""; ""A.1. Computation of the differential of G[sub(n)]""; ""A.2. Second order Taylor expansion of G[sub(n)] in n = 0""
""Appendix B. Formal computation of 3-dimensional waves""""B.1. Formal Fredholm alternative""; ""B.2. Bifurcation equation""; ""Appendix C. Proof of Lemma 3.6""; ""Appendix D. Proofs of Lemmas 3.7 and 3.8""; ""Appendix E. Distribution of Numbers {Ï?[sub(0)]n[sup(2)]}""; ""Appendix F. Pseudodifferential Operators""; ""Appendix G. Dirichlet-Neumann Operator""; ""Appendix H. Proof of Lemma 5.8""; ""Appendix I. Fluid particles dynamics""; ""Bibliography"" |
| Record Nr. | UNINA-9910481020803321 |
|
Iooss Gérard
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Small divisor problem in the theory of three-dimensional water gravity waves / / Gérard Iooss, Pavel I. Plotnikov
| Small divisor problem in the theory of three-dimensional water gravity waves / / Gérard Iooss, Pavel I. Plotnikov |
| Autore | Iooss Gérard |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (144 p.) |
| Disciplina | 532.593 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Water waves
Gravity waves Multiphase flow - Mathematical models Pseudodifferential operators Boundary value problems Bifurcation theory Small divisors |
| ISBN | 1-4704-0554-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""3.3. Main orders of the diffeomorphism and coefficient v""""Chapter 4. Small Divisors. Estimate of L � Resolvent""; ""4.1. Proof of Theorem 4.10""; ""Chapter 5. Descent Method-Inversion of the Linearized Operator""; ""5.1. Descent method""; ""5.2. Proof of Theorem 5.1""; ""5.3. Verification of assumptions of Theorem 5.1""; ""5.4. Inversion of L""; ""Chapter 6. Nonlinear Problem. Proof of Theorem 1.3""; ""Appendix A. Analytical study of G[sub(n)]""; ""A.1. Computation of the differential of G[sub(n)]""; ""A.2. Second order Taylor expansion of G[sub(n)] in n = 0""
""Appendix B. Formal computation of 3-dimensional waves""""B.1. Formal Fredholm alternative""; ""B.2. Bifurcation equation""; ""Appendix C. Proof of Lemma 3.6""; ""Appendix D. Proofs of Lemmas 3.7 and 3.8""; ""Appendix E. Distribution of Numbers {Ï?[sub(0)]n[sup(2)]}""; ""Appendix F. Pseudodifferential Operators""; ""Appendix G. Dirichlet-Neumann Operator""; ""Appendix H. Proof of Lemma 5.8""; ""Appendix I. Fluid particles dynamics""; ""Bibliography"" |
| Record Nr. | UNINA-9910788855903321 |
|
Iooss Gérard
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Small divisor problem in the theory of three-dimensional water gravity waves / / Gérard Iooss, Pavel I. Plotnikov
| Small divisor problem in the theory of three-dimensional water gravity waves / / Gérard Iooss, Pavel I. Plotnikov |
| Autore | Iooss Gérard |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (144 p.) |
| Disciplina | 532.593 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Water waves
Gravity waves Multiphase flow - Mathematical models Pseudodifferential operators Boundary value problems Bifurcation theory Small divisors |
| ISBN | 1-4704-0554-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""3.3. Main orders of the diffeomorphism and coefficient v""""Chapter 4. Small Divisors. Estimate of L � Resolvent""; ""4.1. Proof of Theorem 4.10""; ""Chapter 5. Descent Method-Inversion of the Linearized Operator""; ""5.1. Descent method""; ""5.2. Proof of Theorem 5.1""; ""5.3. Verification of assumptions of Theorem 5.1""; ""5.4. Inversion of L""; ""Chapter 6. Nonlinear Problem. Proof of Theorem 1.3""; ""Appendix A. Analytical study of G[sub(n)]""; ""A.1. Computation of the differential of G[sub(n)]""; ""A.2. Second order Taylor expansion of G[sub(n)] in n = 0""
""Appendix B. Formal computation of 3-dimensional waves""""B.1. Formal Fredholm alternative""; ""B.2. Bifurcation equation""; ""Appendix C. Proof of Lemma 3.6""; ""Appendix D. Proofs of Lemmas 3.7 and 3.8""; ""Appendix E. Distribution of Numbers {Ï?[sub(0)]n[sup(2)]}""; ""Appendix F. Pseudodifferential Operators""; ""Appendix G. Dirichlet-Neumann Operator""; ""Appendix H. Proof of Lemma 5.8""; ""Appendix I. Fluid particles dynamics""; ""Bibliography"" |
| Record Nr. | UNINA-9910827765403321 |
|
Iooss Gérard
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
