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 ...
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...
doi:10.1007/978-3-642-65690-3_31Gustav DoetschSpringer Berlin Heidelberg
Introduction to the Theory and Application of the Laplace Transformation; Springer: Berlin/Heidelberg, Germany, 1974. [Google Scholar] Lundberg, K.H.; Miller, H.R.; Trumper, D.L. Initial conditions, generalized functions, and the Laplace transform: Troubles at the origin. IEEE Control Syst. ...
Introduction to the Theory and Application of the Laplace Transformation; Springer: Berlin/Heidelberg, Germany, 1974. [Google Scholar] Lundberg, K.H.; Miller, H.R.; Trumper, D.L. Initial conditions, generalized functions, and the Laplace transform: Troubles at the origin. IEEE Control Syst. ...
Introduction to the Theory and Application of the Laplace Transformation; Springer: Berlin/Heidelberg, Germany, 1974. [Google Scholar] Lundberg, K.H.; Miller, H.R.; Trumper, D.L. Initial conditions, generalized functions, and the Laplace transform: Troubles at the origin. IEEE Control Syst. ...