The Complex Inversion Formula for the Absolutely Converging Laplace Transformation. The Fourier TransformationHitherto, without exception, we determined the image function F ( s ) of some given original function f ( t ). Clearly, often one is faced with the inverse problem, that is to find the...
The inversion formula of Theorem 24.4 is contingent on two restricting hypotheses: L { f } must have a half-plane of absolute convergence, and f must be of bounded variation near the point t where f ( t ) is to be evaluated. Using the Integration Theorem 8.1, we can develop an ...
doi:10.1007/978-3-642-65690-3_31Gustav DoetschSpringer Berlin Heidelberg