## Introduction to the Theory of Hyperfunctions |

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### Contents

V | 11 |

VI | 16 |

VII | 19 |

VIII | 34 |

IX | 37 |

X | 41 |

XI | 47 |

XII | 55 |

XXXII | 259 |

XXXIII | 263 |

XXXIV | 276 |

XXXV | 281 |

XXXVI | 287 |

XXXVII | 294 |

XXXVIII | 301 |

XXXIX | 310 |

### Common terms and phrases

algebraic analytically continued assume boundary values boundary-value representation Chapter choose closed set coefficients compact set compact support complex neighborhood compute connected component consider continuous function converges locally uniformly convex cone coordinate transformation Corollary corresponding decompose defining function definition denote differential operator element embedding equal equation estimate example Exercise exists exponentially decreasing Fj(z flabby resolution formula Fourier hyperfunctions Fourier transform germs given global Hence holomorphic function holomorphic parameter hyper hyperfunction inductive limit infinitesimal wedge integral path inverse isomorphism Lemma linear long exact sequence mapping micro-analytic microfunctions Note obtain open set origin polydisc polynomials presheaf proof of Theorem Proposition Radon decomposition real analytic function real analytic parameter real axis respect restriction result right-hand side rs(x Runge domain satisfies single-variable singular spectrum singular support slowly increasing hyperfunction Stein open set subset sufficiently supp support contained surjective term topological space topology variables vector

### Popular passages

Page vi - ... and concepts of one field of enquiry have and have had on the development of another. The Mathematics and Its Applications programme tries to make available a careful selection of books which fit the philosophy outlined above. With such books, which are stimulating rather than definitive, intriguing rather than encyclopaedic, we hope to contribute something towards better communication among the practitioners in diversified fields.

Page vi - As long as algebra and geometry proceeded ics in science ... along separate paths, their advance was slow and their applications limited. Eugene Wigner But when these sciences joined company they drew from each other fresh vitality and Well, if you know of a better 'ole, go to it. thenceforward marched on at a rapid pace towards perfection. Bruce Bairnsfather Joseph Louis Lagrange. What is now proved was once only imagined.

Page v - completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics. This programme, Mathematics and Its Applications, is devoted to new emerging (sub)disciplines and to such (new) interrelations as exempla gratia: - a central concept which plays an important role in several different mathematical and/or scientific specialized areas; - new applications of the...

Page v - Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years:...

Page v - The one that they can't see the problem. day, perhaps you will find the final question. GK Chesterton. The Scandal of Father Brown 'The Point of a Pin'. The Hermit Clad in Crane Feathers

Page v - EDITOR'S PREFACE Approach your problems from the right end and begin with the answers. Then one day, perhaps you will find the final question. The Hermit Clad in Crane Feathers

Page 447 - Theory of (vector valued) Fourier hyperfunctions. Their realization as boundary values of (vector valued) slowly increasing holomorphic functions. III".