Fourier series oor Nederlands

Fourier series

naamwoord
en
(mathematics) A series of cosine and sine functions or complex exponentials resulting from the decomposition of a periodic function.

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Fourierreeks

naamwoord
en
series of cosine and sine functions
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Fourier cosine series
Fourier-cosinusreeks
Fourier sine series
Fourier-sinusreeks

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The Fourier series?
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I haven't been able to figure out the Fourier series for it yet.
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Fourier series: Describes periodical functions as a series of sine and cosine functions.
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Cantor would, in his study of Fourier series, consider point sets in Euclidean space.
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In 1898, Albert A. Michelson developed a device that could compute and re-synthesize the Fourier series.
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Recall that a Fourier series is only suitable to the analysis of periodic (or finite-domain) functions f(x) with period 2π.
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Spectrum continuation analysis (SCA) is a generalization of the concept of Fourier series to non-periodic functions of which only a fragment has been sampled in the time domain.
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Inspired by the work of his mentor in Paris, Dirichlet published in 1829 a famous memoir giving the conditions, showing for which functions the convergence of the Fourier series holds.
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In the theory of Hardy spaces, Carleson's contributions include the corona theorem (1962) and establishing the almost everywhere convergence of Fourier series for square-integrable functions (now known as Carleson's theorem).
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However, the axioms of determinacy and dependent choice together are sufficient for most geometric measure theory, potential theory, Fourier series and Fourier transforms, while making all subsets of the real line Lebesgue-measurable.
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At the location of the discontinuity itself, the partial Fourier series will converge to the midpoint of the jump (regardless of what the actual value of the original function is at this point).
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It is important to put emphasis on the word finite because even though every partial sum of the Fourier series overshoots the function it is approximating, the limit of the partial sums does not.
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Now, any periodic potential V(r) which shares the same periodicity as the direct lattice can be expanded out as a Fourier series whose only non-vanishing components are those associated with the reciprocal lattice vectors.
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In mathematics, the Gibbs phenomenon, discovered by Henry Wilbraham (1848) and rediscovered by J. Willard Gibbs (1899), is the peculiar manner in which the Fourier series of a piecewise continuously differentiable periodic function behaves at a jump discontinuity.
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While trying to gauge the range of functions for which convergence of the Fourier series can be shown, Dirichlet defines a function by the property that "to any x there corresponds a single finite y", but then restricts his attention to piecewise continuous functions.
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It also introduced the Dirichlet function as an example of a function that is not integrable (the definite integral was still a developing topic at the time) and, in the proof of the theorem for the Fourier series, introduced the Dirichlet kernel and the Dirichlet integral.
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Series, Fourier analysis, functional analysis
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In pure mathematics, his most important works were his series of memoirs on definite integrals and his discussion of Fourier series, the latter paving the way for the classic researches of Peter Gustav Lejeune Dirichlet and Bernhard Riemann on the same subject; these are to be found in the Journal of the École Polytechnique from 1813 to 1823, and in the Memoirs de l'Académie for 1823.
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Inspired by some correspondence in Nature between Michelson and Love about the convergence of the Fourier series of the square wave function, in 1898 J. Willard Gibbs published a short note in which he considered what today would be called a sawtooth wave and pointed out the important distinction between the limit of the graphs of the partial sums of the Fourier series, and the graph of the function that is the limit of those partial sums.
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Pontryagin duality places in a unified context a number of observations about functions on the real line or on finite abelian groups: Suitably regular complex-valued periodic functions on the real line have Fourier series and these functions can be recovered from their Fourier series; Suitably regular complex-valued functions on the real line have Fourier transforms that are also functions on the real line and, just as for periodic functions, these functions can be recovered from their Fourier transforms; and Complex-valued functions on a finite abelian group have discrete Fourier transforms which are functions on the dual group, which is a (non-canonically) isomorphic group.
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Fourier Analysis (theory and applications of Fourier series). Bachelor Colloquium
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Fourier series and other representations of analytic functions of one real variable (Pisa, T. Nistri, 1880)
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The following pages link to Fourier series:
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Among his lesser known works: A failed attempt to use a Fourier series to explain the pattern of a zebra's stripes.
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37 sinne gevind in 12 ms. Hulle kom uit baie bronne en word nie nagegaan nie.