EMIS ELibM Electronic Journals Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 4, pp. 1031-1038 (1999)

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A Real Inversion Formula for the Laplace Transform in a Sobolev Space

K. Amano, S. Saitoh and A. Syarif

All authors: Gunma Univ. Japan, Dept. Math., Fac. Eng., Kiryu, 376-8515, Japan

Abstract: For the real-valued Sobolev-Hilbert 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

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Electronic fulltext finalized on: 7 Aug 2001. This page was last modified: 9 Nov 2001.

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