## Integral Transforms of Generalized FunctionsEnglish translation (from revised and enlarged versions of the Russian editions of 1977 and 1984) of a reference work which makes available to engineers, physicists and applied mathematicians theoretical and tabular material pertaining to certain extensions of standard integral transform techniques. Diverse transforms are touched upon, but the emphasis (particularly in the tables) is on generalized Fourier and Laplace transforms. Some multi-dimensional results are presented. Expensive, but nicely produced, and redundant with nothing standard to the reference shelves of mathematical libraries. (NW) Annotation copyrighted by Book News, Inc., Portland, OR |

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### Contents

The Fourier Transformation | 19 |

The Laplace and Mellin Transformations | 27 |

The Stieltjes Hilbert and Related | 47 |

The Weierstrass Transformation | 67 |

The Bessel Transformations | 73 |

Transformations Involving | 109 |

The G and Htransformations | 131 |

Tables of Fourier Transforms | 148 |

Tables of Rightsided Laplace | 297 |

316 | |

List of Notation | 334 |

340 | |

### Common terms and phrases

analytic Asymptotic expansion bounded called collection of seminorms complex number complex-valued smooth functions considered constant convolution countable collection defined definition denotes the dual element Estimate exists extended f F[f finite fixed real number following imbeddings Fourier transformation given Hankel transformation Hilbert transform imbeddings are valid integral transforms inversion formula kind Laplace transform linear space locally integrable function mapping Mellin transform Moreover nonnegative integer obtained operation-transform formulas operator ordinary function f(t otherwise Pandey points polynomial properties proved respect restricted ordinary function sense of convergence sense of equality sequence sgnt sin ax slow growth smooth functions o(t Stieltjes transform structure suitably restricted ordinary supp Suppose test-function space theorems topology Uniqueness values x+io zel2 zel2g Zemanian