Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 4, pp. 10311038 (1999) 

A Real Inversion Formula for the Laplace Transform in a Sobolev SpaceK. Amano, S. Saitoh and A. SyarifAll authors: Gunma Univ. Japan, Dept. Math., Fac. Eng., Kiryu, 3768515, JapanAbstract: For the realvalued SobolevHilbert space on $[0,\infty)$ comprising absolutely continuous functions $F = F(t)$ normalized by $F(0) = 0$ and equipped with the inner product $(F_1,F_2) = \int_0^\infty (F_1(t)F_2(t) + F_1'(t)F_2'(t))\,dt$ we shall establish a real inversion formula for the Laplace transform. Keywords: laplace transform, real inversion formula, Sobolev space, reproducing kernel, Mel\lin transform, Szegö space Classification (MSC2000): 44A10, 30C40 Full text of the article:
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