## Distributions and the boundary values of analytic functionsThe volume succeeds in covering, in a highly compact format, virtually every important feature of harmonic analysis, while presenting the material at an introductory level throughout. To make the survey simple and self-contained, the author has wherever possible defined concepts and given proofs in great detail. The Fourier Transform on the Real Line for Functions in L sub 1. The Fourier Transform on the Real Line for Functions in L sub 2. Regular Points and Spectrum. More on the Gel'fand Theory and an Introduction to Point Set Topology. Further Topological Notions. Compactness of the Space of Maximal Ideals over a Banach Algebra. An Introduction to Topological Groups and Star Algebras. The Quotient Group of a Topological Group and Some Further Topological Notions. Right Haar Measures and the Haar Covering Function. The Existence of a Right Invariant Haar Integral Over any Locally Compact Topological Group. The Daniell Extension from a Topological Point of View, Some General Results from Measure Theory, and Group Algebras. Characters and the Dual Group of a Locally Compact, Abelian, Topological Group. Generalization of the Fourier Transform to L sub 1(G) and L sub 2(G). |

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### Contents

Distributions | 1 |

The Laplace Transform | 45 |

Distributional Boundary Values of Analytic Functions | 55 |

Copyright | |

2 other sections not shown

### Common terms and phrases

analytic continuation analytic functions boundary behavior Cauchy integral causal Chapter characterization classic compact set compact support constant converge to zero convolution Corollary Cq is dense Cq(K defined denote dissipative operator distributional boundary values domain dual dual space established exists extended f(p)eH+ fact finite following theorem formula Fourier transform functional on Cq given Green's function H+ function half plane Hence Hilbert transform holomorphic functions ij/j implies L2 norm Laplace transform Lemma mapping Moreover n x n matrix nonnegative definite numbers obtain open set p e Cq passive immittance operator polynomial positive real positive-real proof of Theorem pv 1/co real axis result satisfies scalar Schwartz seminorms sequence shows solution subspace supp support is contained testing functions Theorem 3.2 topology u e 2'Ll uniformly bounded unique weak derivative weak topology Wkr(p Wohlers