Results 151 to 160 of about 4,676,398 (193)

The Expression of Trigonometrical Series in Fourier Form

Canadian Journal of Mathematics, 1960
In a paper published in 1936 Burkill (2) proved that, if the trigonometrical series1.1is bounded except on a countable set and if the series obtained by integrating series (1.1) once converges everywhere, then the coefficients can be written in Fourier form using the C1P-integral.
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Trigonometric Series and Fourier Series

1979
D. Bernoulli, D’ Alembert, Lagrange, and Euler, from about 1740 onward, were led by problems in mathematical physics to consider and discuss heatedly the possibility of representing a more or less arbitrary function f with period 2n as the sum of a trigonometric series of the form $$\frac{1}{2} {{a}_{0}} + \sum\limits_{{n = 1}}^{{}} {\left( {{{a}_ ...
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On Cesàro Means of Double Trigonometric Fourier Series

Mathematical Notes, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ON THE BEHAVIOUR OF THE PARTIAL SUMS OF TRIGONOMETRIC FOURIER SERIES

Russian Mathematical Surveys, 1968
In this paper we give a detailed exposition of Carleson's method of estimating partial sums of trigonometric Fourier series of functions that belong to the class , . We also improve slightly Carleson's relevant result by giving, instead of an estimate almost everywhere of the rate of growth of the partial sums of a Fourier series, an integral estimate ...
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Random Fourier Series and Trigonometric Sums, I

2014
In Chapter 3 we investigate Gaussian processes in “the stationary case,” where e.g. the underlying space is a compact group and the distance is translation invariant. This is relevant to the study of random Fourier series, the basic example of which is X t =∑ k≥1 ξ k exp(2P iikt), where t∈[0,1] and the r.v.s ξ k are independent.
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Euler‐Maclaurin Summation of Trigonometric Fourier Series

Studies in Applied Mathematics, 1994
Trigonometric Fourier series are, in general, difficult to sum to high accuracy. An example is given by the series urn:x-wiley:00222526:media:sapm1994923213:sapm1994923213-math-0001 in which α and β(>0) are rational numbers satisfying 0<β/α≤1, where λ is an independent variable and j is a positive integer or zero. This paper presents a method for
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Summation of trigonometric series by Fourier transforms

Applied Mathematics and Mechanics, 1989
The author has obtained summation of a number of trigonometric series by using various Fourier transforms contained in \textit{A. Erdélyi}, \textit{W. Magnus}, \textit{F. Oberhettinger} and \textit{F. G. Tricomi}: ``Tables of integral transforms'' Vol. I (1954; Zbl 0055.36401); Vol. II (1954; Zbl 0058.34103).
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ON THE CONVERGENCE OF DOUBLE TRIGONOMETRIC SERIES AND FOURIER SERIES WITH MONOTONE COEFFICIENTS

Mathematics of the USSR-Sbornik, 1987
The author considers different conditions on the coefficients of double Fourier series which lead to the Fourier series of functions \(f\in L_ p(0,2\pi)\) 2 or to the convergence series. He shows that some of these results cannot be improved.
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Riemann summability of multi-dimensional trigonometric-fourier series

Approximation Theory and its Applications, 1998
Suppose \(00\), \(j=1,\dots,d.\) In this paper the author deals with the limit of \({\widetilde S}^j_\mu f\) \(( j=0,1,\dots,d)\) in some norm as \(\mu\to 0\) under the restriction \[ \tau^{-1}\leq {\mu_k\over\mu_j}\leq \tau,\quad j,k=1,\dots,d\quad (\tau\geq 1).
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On strong convergence of trigonometric and Fourier series

Acta Mathematica Hungarica, 1983
A real or complex valued sequence \((s_ k)\) is (i) strongly \(C_ 1- summable\) to t with index \(\lambda>0\) (or \((s_ k)\to t[C_ 1]_{\lambda})\) if \(\sum^{n}_{k=0}| s_ k- t|^{\lambda}=o(n) (n\to \infty)\) and (ii) strongly convergent to t with index \(\lambda>0\) (or \((s_ k)\to t[I]_{\lambda})\) if and only if \((s_ n)\) converges to t and \(\sum ...
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