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Almost periodic generalized functions

Published online by Cambridge University Press:  24 October 2008

H. Burkill
Affiliation:
University of Sheffield
B. C. Rennie
Affiliation:
James Cook University of North Queensland

Extract

In (4) a space C of generalized functions was defined which is rather larger than the simple space used to such effect by Lighthill in (3). At the core of C is the space C0 = T of test functions. These are entire (complex) functions f such that all derivatives of f and its Fourier transform F have order of magnitude not exceeding as x → ± ∞, where c is a positive number depending on the individual derivative concerned. If f, gT, the inner product 〈f | g〉 is defined to be

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

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