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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 4, 1999, pp. 1031–1038
DOI: 10.4171/ZAA/926

Published online: 1999-12-31

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

Kazuo Amano[1], S. Saitoh[2] and A. Syarif[3]

(1) Gunma University, Kiryu, Japan
(2) Gunma University, Kiryu, Japan
(3) Gunma University, Kiryu, Japan

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 $(F_1, F_2) = \int^{\infty}_0 (F_1(t)F_2(t) + F'_1(t)F'_2(t))dt$ we shall establish a real inversion formula for the Laplace transform.

Keywords: Laplace transform, real inversion formula, Sobolev space, reproducing kernel, Mellin transform, Szegö space

Amano Kazuo, Saitoh S., Syarif A.: A Real Inversion Formula for the Laplace Transform in a Sobolev Space. Z. Anal. Anwend. 18 (1999), 1031-1038. doi: 10.4171/ZAA/926