The Inversion Theorem

  • B. Davies
Part of the Applied Mathematical Sciences book series (AMS, volume 25)


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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  1. 1.
    For a thorough treatment of the material in Sections 2.1–2.3, see, for example, APOSTOL (1957), Ch. 15.Google Scholar
  2. 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

Authors and Affiliations

  • B. Davies
    • 1
  1. 1.The Australian National UniversityCanberraAustralia

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