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
For a thorough treatment of the material in Sections 2.1–2.3, see, for example, APOSTOL (1957), Ch. 15.
Often known as the Heaviside series expansion. See Section 6.5 for the general case.
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© 1978 Springer Science+Business Media New York
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Davies, B. (1978). The Inversion Theorem. In: Integral Transforms and Their Applications. Applied Mathematical Sciences, vol 25. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5512-1_2
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DOI: https://doi.org/10.1007/978-1-4757-5512-1_2
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