## Analytic Extension Formulas and their ApplicationsS. Saitoh, N. Hayashi, M. Yamamoto Analytic Extension is a mysteriously beautiful property of analytic functions. With this point of view in mind the related survey papers were gathered from various fields in analysis such as integral transforms, reproducing kernels, operator inequalities, Cauchy transform, partial differential equations, inverse problems, Riemann surfaces, Euler-Maclaurin summation formulas, several complex variables, scattering theory, sampling theory, and analytic number theory, to name a few. Audience: Researchers and graduate students in complex analysis, partial differential equations, analytic number theory, operator theory and inverse problems. |

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### Contents

Representations of analytic functions on typical domains | 15 |

Uniqueness in determining damping coefficients | 26 |

Analytic continuation of Cauchy and exponential | 47 |

B Gustafsson and M Putinar | 57 |

A sampling principle associated with Saitohs fundamental | 73 |

The enclosure method and its applications | 87 |

On analytic properties of a multiple Lfunction 105 | 104 |

H Ishikawa | 121 |

H Isozaki | 164 |

Extension and division on complex manifolds 189 | 193 |

Analytic extension formulas integral transforms | 207 |

Analytic continuation beyond the ideal boundary | 233 |

Justification of a formal derivation of the EulerMaclaurin | 251 |

The CalogeroMoser model the Calogero model and analytic | 271 |

### Other editions - View all

Analytic Extension Formulas and their Applications S. Saitoh,N. Hayashi,M. Yamamoto Limited preview - 2001 |

Analytic Extension Formulas and Their Applications S. Saitoh,N. Hayashi,M. Yamamoto No preview available - 2014 |

Analytic Extension Formulas and their Applications S. Saitoh,N. Hayashi,M. Yamamoto No preview available - 2010 |

### Common terms and phrases

2001 Kluwer Academic analytic continuation Analytic Extension Formulas analytic function Applications assume Bergman bounded holomorphic function Carleman estimate Cauchy problem compact Complex Variables condition constant construct convergence defined denote derivative differential equations Dirichlet entire functions Euler–Maclaurin summation formula expansion exponential transform Faddeev Fourier transform function f global existence Hayashi Hence Hilbert space holomorphic functions hyperbolic ideal boundary inequality inverse problem inversion formula Kluwer Academic Publishers Korteweg–de Vries equation Lemma linear Math Mathematics meromorphic continuation meromorphic function monotone function multi-dimensional inverse nonlinear Schrödinger equations norm obtain operator monotone operator monotone functions orthogonal plane polynomials proof of Theorem proved pseudoconvex domain quadrature domain reproducing kernel resp result Riemann mapping function Saitoh sampling satisfying scattering amplitude scattering theory Schrödinger operator strictly pseudoconvex domains subvarieties Taylor coefficients tions uniqueness unit disc