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A note on the representation of functions by absolutely convergent fourier integrals

Published online by Cambridge University Press:  24 October 2008

H. R. Pitt
H. R. Pitt
Affiliation:
Queen's UniversityBelfast
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Extract

1. We write L for the class of integrable functions in (− ∞, ∞), V for the class of functions of bounded variation, and define A, A to be the classes of functions F(x) which may be expressed in the forms

respectively.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 44 , Issue 1 , January 1948 , pp. 8 - 12
Copyright
Copyright © Cambridge Philosophical Society 1948

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References

† Integrals without specified limits are over the range (− ∞, ∞).

‡ Wiener, N., The Fourier Integral (Cambridge, 1933), Lemma 67, p. 80.Google Scholar

§ Wiener, N. and Pitt, H. R., ‘On absolutely convergent Fourier-Stieltjes transforms’, Duke Math. J. 4 (1938), 420–35,CrossRefGoogle Scholar Lemma 1.

† Bochner, S., Fouriersche Integrale (Leipzig, 1932),Google Scholar Theorem 24 of § 21.

‡ Besicovitch, S., Almost Periodic Functions (Cambridge, 1932), § 3.Google Scholar