On approximation by trigonometric sums
نویسندگان
چکیده
منابع مشابه
On Some Trigonometric Power Sums
In contrast to Fourier series, these finite power sums are over the angles equally dividing the upper-half plane. Moreover, these beautiful and somewhat surprising sums often arise in analysis. In this note, we extend the above results to the power sums as shown in identities (17), (19), (25), (26), (32), (33), (34), (35), and (36) and in the appendix. The method is based on the generating func...
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A well known theorem states as follows :' Let ni < n2 <. . ., nk+1 / nk > A > 1 be an infinite sequence of real numbers and S (ak + bk) a divergent series satisfying k=1 Then denotes the Lebesgue measure of the set in question. It seems likely that the Theorem remains true if it is not assumed that the n k are integers. On the other hand if nk ,f-n,.-1 is an arbitrary sequence of integers it is...
متن کاملSome Notes on Trigonometric Sums
1 Trigonometric Sums 1 1.1 Gauss Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Kloosterman Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Geometrization 2 2.1 A Lemma on Torsors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Artin-Shreier Sheaves . . . . . . . . . . . . . . . . . ...
متن کاملApproximation By Trigonometric Polynomials
These notes are prepared as lecture notes exclusively for the participants of this conference only. Any reproduction in any media, or any use for any other purpose of any part of this manuscript, without an expressed written consent of the author is unlawful.thorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conc...
متن کاملOn trigonometric sums with random frequencies
There is a wide and nearly complete theory of trigonometric series with random coefficients; on the other hand, much less is known on trigonometric series with random frequencies. In this paper we study the asymptotic behavior of SN = ∑N k=1 sinnkx for random sequences (nk)k≥1, independent and identically distributed over disjoint intervals Ik ⊂ (0,∞) of the same length. As it turns out, the be...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1914
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1914-02562-5