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Fourier-Laplace transforms decaying exponentially

Published online by Cambridge University Press:  24 October 2008

H. Kaneta
H. Kaneta
Affiliation:
Department of Mathematics, Okayama University, Okayama 700, Japan
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Extract

Let ƒ(x) be a C-valued function which is integrable with respect to a positive measure m on the Borel σ-field of R = (– ∞, ∞). We shall give necessary and sufficient conditions under which the following Fourier-Laplace transform f(λ) of ƒ(x) decays exponentially as λ → ∞:

where θ is a constant with –π/2 ≤ θ ≤ π/2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 2 , March 1988 , pp. 321 - 322
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

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