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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 1, 2001, pp. 193–202
DOI: 10.4171/ZAA/1010

Published online: 2001-03-31

Conditional Stability of a Real Inverse Formula for the Laplace Transform

S. Saitoh[1], Vu Kim Tuan[2] and Masahiro Yamamoto[3]

(1) Gunma University, Kiryu, Japan
(2) Kuwait University, Safat, Kuwait
(3) University of Tokyo, Japan

We establish a conditional stability estimate of a real inverse formula for the Laplace transform of functions under the assumption that the Bergman-Selberg norms of the Laplace transform of those functions are uniformly bounded. The rate of the stability estimate is shown to be of logarithmic order.

Keywords: Laplace transform, real inversion formulas, conditional stability, Bergman-Selberg space, error estimates, Mellin transform, Gauss formula, convolution, reproducing kernels

Saitoh S., Kim Tuan Vu, Yamamoto Masahiro: Conditional Stability of a Real Inverse Formula for the Laplace Transform. Z. Anal. Anwend. 20 (2001), 193-202. doi: 10.4171/ZAA/1010