Integrals and Summable Trigonometric Series
نویسنده
چکیده
is that of suitably defining a trigonometric integral with the property that, if the series (1.1) converges everywhere to a function ƒ(x), then f(x) is necessarily integrable and the coefficients, an and bn, given in the usual Fourier form. It is well known that a series may converge everywhere to a function which is not Lebesgue summable nor even Denjoy integrable (completely totalisable, [3]). A simple example is that given by Fatou in which an = 0, w^O, and &n = l/log (n + l),
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