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Almost periodic generalized functions
Published online by Cambridge University Press: 24 October 2008
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, g∈ T, the inner product 〈f | g〉 is defined to be
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 1 , July 1983 , pp. 149 - 166
- Copyright
- Copyright © Cambridge Philosophical Society 1983
References
REFERENCES
(2)Doherty, I. W. Almost periodic generalized functions (Ph.D. thesis, University of Melbourne, 1973).Google Scholar
(3)Lighthill, M. J.Fourier analysis and generalised functions (Cambridge University Press, 1958).Google Scholar