## Introduction to Hyperfunctions and Their Integral Transforms: An Applied and Computational ApproachThis textbook presents an introduction to the subject of generalized functions and their integral transforms by an approach based on the theory of functions of one complex variable. It includes many concrete examples. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Chapter 1 Introduction to Hyperfunctions | 1 |

Chapter 2 Analytic Properties | 63 |

Chapter 3 Laplace Transforms | 155 |

Chapter 4 Fourier Transforms | 241 |

Chapter 5 Hilbert Transforms | 275 |

Chapter 6 Mellin Transforms | 309 |

Chapter 7 Hankel Transforms | 337 |

Appendix A Complements | 373 |

Appendix B Tables | 394 |

407 | |

List of Symbols | 410 |

413 | |

### Other editions - View all

Introduction to Hyperfunctions and Their Integral Transforms: An Applied and ... Urs Graf Limited preview - 2010 |

### Common terms and phrases

analytic continuation arbitrary assume change of variables closed contour compact complex plane Consider contour integral converges uniformly correspondence deﬁned defining function F(z Deﬁnition denoted differential Dirac impulse domain entire function equivalent defining function established Example exists F_(z F+(z fc=i ﬁnite Fourier series Fourier transform given hyperfunction Hankel transform Hilbert transform holomorphic function holomorphic hyperfunction hyperfunction f(x hyperfunctions deﬁned image function integral equation integrand interval Let f(x Let us compute log(z loop lower component lower half-plane lower hyperfunctions Mellin transform obtain ordinary function parameter periodic hyperfunction polynomial Problem Proof Proposition real analytic function real axis respect right-hand side right-sided sense of hyperfunctions sgn(x shows Similarly sin(a7r singular solution strip of convergence strong defining function theorem Transforms of Hyperfunctions uniform convergence upper and lower upper half-plane write yields zero