Distributions and the Boundary Values of Analytic Functions

Abstract : The 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).