For the real-valued Sobolev-Hilbert space on comprising absolutely continuous functions normalized by and equipped with the inner product we shall establish a real inversion formula for the Laplace transform.
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Kazuo Amano, S. Saitoh, A. Syarif, A Real Inversion Formula for the Laplace Transform in a Sobolev Space. Z. Anal. Anwend. 18 (1999), no. 4, pp. 1031–1038DOI 10.4171/ZAA/926