JournalszaaVol. 18, No. 4pp. 1031–1038

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

  • Kazuo Amano

    Gunma University, Kiryu, Japan
  • S. Saitoh

    Gunma University, Kiryu, Japan
  • A. Syarif

    Gunma University, Kiryu, Japan
A Real Inversion Formula for the Laplace Transform in a Sobolev Space cover
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Abstract

For the real-valued Sobolev-Hilbert space on (0,)(0, \infty) comprising absolutely continuous functions F=F(t)F = F(t) normalized by F(0)=0F(0) = 0 and equipped with the inner product (F1,F2)=0(F1(t)F2(t)+F1(t)F2(t))dt(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.

Cite this article

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. 1031–1038

DOI 10.4171/ZAA/926