## Abstract

As necessary preliminaries to a statement and proof of the inversion theorem, which together with its elementary properties makes the Laplace transform a powerful tool in applications, we must first take note of some results from classical analysis.^{1} Suppose that f(x) is a function continuous on the closed interval a ≤ x ≤ b (and hence uniformly continuous).

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## Footnotes

- 1.For a thorough treatment of the material in Sections 2.1–2.3, see, for example, APOSTOL (1957), Ch. 15.Google Scholar
- 2.Often known as the Heaviside series expansion. See Section 6.5 for the general case.Google Scholar

## Copyright information

© Springer Science+Business Media New York 1978