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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Abstract. The paper is related to the following question of P. L. Ul’yanov: is it true that for any 2π-periodic continuous function f there is a uniformly convergent rearrangement of its trigonometric Fourier series? In particular, we give an affirmative answer if the absolute values of Fourier coefficients of f decrease. Also, we study a problem how to choose m terms of a trigonometric polynom...
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where E c [0, 1] is any given set o f positive measure and {ak} any given sequence of real numbers. This theorem was first proved by R. Salem and A. Zygmund in case of a -0, where {flk} satisfies the so-called Hadamard's gap condition (cf. [4], (5.5), pp. 264-268). In that case they also remarked that under the hypothesis (1.2) the condition (1.3) is necessary for the validity of (1.5) (cf. [4]...
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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: Journal of Mathematical Analysis and Applications
سال: 1978
ISSN: 0022-247X
DOI: 10.1016/0022-247x(78)90245-7