## An introduction to transform theoryAn introduction to transform theory |

### What people are saying - Write a review

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

### Contents

1 | |

Chapter 2 Dirichlet Series | 19 |

Chapter 3 The Zeta Function | 51 |

Chapter 4 The Prime Number Theorem | 69 |

Chapter 5 The Laplace Transform | 93 |

Chapter 6 Real Inversion Theory | 133 |

Chapter 7 The Convolution Transform | 169 |

Chapter 8 Tauberian Theorems | 193 |

Chapter 9 Inversion by Series | 219 |

243 | |

247 | |

254 | |

### Other editions - View all

Pure and Applied Mathematics: A Series of Monographs and Textbooks, Volume 42 David Vernon Widder No preview available - 1949 |

Pure and Applied Mathematics: A Series of Monographs and Textbooks, Volume 42 No preview available - 1949 |

Pure and Applied Mathematics: A Series of Monographs and Textbooks, Volume 42 No preview available - 1949 |

### Common terms and phrases

Abel summability Abel’s absolute convergence analog apply Theorem arbitrary assume become inﬁnite bounded variation change of variable Chapter completely monotonic completes the proof compute conclusion of Theorem constant converges absolutely converges uniformly convolution transform Corollary corresponding D. V. Widder deﬁned Deﬁnition derivative determining function differential equation Dirichlet series diverges dt converges entire function example Exercise factor ﬁnd ﬁnite ﬁrst following theorem frequency function function f G. H. Hardy half-plane Hence hypothesis implies inequality integral converging absolutely integral sign integrand inversion function kernel Laplace integral Laplace transform Lemma limit linear notation obtain oc(t oz(t polynomial positive integers positive number potential transform power series prime number theorem proof is complete replaced representation Riemann right-hand side satisﬁes sequence solution someM Stieltjes transform Tauberian theorem term Theorem 7.1 theory valid veriﬁed vertical line zeta-function