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The Laplace Transform
Chapter 1II Distributional Boundary Values of Analytic Functions
2 other sections not shown
analytic continuation analytic functions arbitrary boundary behavior Cauchy integral causal Chapter characterization classic compact set compact support constant continuous linear functional converge to zero convolution Corollary CQ is dense defined denote dissipative operator distributional boundary values domain dual dual space established exists extended fact finite following theorem formula Fourier transform functional on CJ given Green's function H+ function half plane Hence Hilbert transform holomorphic functions implies L2 norm Laplace transform Lemma Let u e linear space mapping Moreover n x n matrix nonnegative definite numbers obtain open interval open set p e CQ passive immittance operator polynomial positive real positive-real proof of Theorem real axis result satisfies scalar Schwartz seminorms sequence shows solution subspace supp support is contained testing functions Theorem 3.2 topology uniformly bounded unique weak derivative weak topology Wohlers