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Published online by Cambridge University Press: 24 October 2008
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.
† 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
