On the introduction of convergence factors into summable series and summable integrals
نویسندگان
چکیده
منابع مشابه
Integrals and Summable Trigonometric Series
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])...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1907
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1907-1500786-6