Integrals and summable trigonometric series
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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Let N be the set of positive integers. A function from N to a set is called a sequence. If X is a topological space and x ∈ X, a sequence a : N → X is said to converge to x if for every open neighborhood U of x there is some NU such that n ≥ NU implies that an ∈ U . If there is no x ∈ X for which a converges to x, we say that a diverges. Let a : N→ R. We define s(a) : N→ R by sn(a) = ∑n k=1 ak....
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1955
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1955-09853-7