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On the Laplace transform

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Published/Copyright: April 24, 2024

Abstract

Sufficient conditions are given for a function F ( p ) to be the Laplace transform of a function f ( t ) or a distribution f. No assumption on f is given a priori. It is not even assumed that f = 0 for t < 0 .

MSC 2020: 44A10

References

[1] H. Bateman and A. Erdelyi, Tables of Integral Transforms, McGraw-Hill, New York, 1954. Search in Google Scholar

[2] L. Hörmander, The Analysis of Linear Partial Differential Operators. Vol. 1, Springer, New York, 1983. Search in Google Scholar

[3] A. G. Ramm, Analysis of the Navier–Stokes Problem. Solution of a Millennium Problem, Springer, Cham, 2023. 10.1007/978-3-031-30723-2Search in Google Scholar

[4] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1974. Search in Google Scholar

[5] J. Schiff, The Laplace Transform, Springer, Berlin, 1999. 10.1007/978-0-387-22757-3Search in Google Scholar

Received: 2024-01-06
Revised: 2024-03-31
Accepted: 2024-03-31
Published Online: 2024-04-24
Published in Print: 2024-12-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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