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Vol 4 Iss. 1
Pages:
54-62
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RUS
Article

On the theory of trigonometric series

Authors:
N. M. Krylov
Date submitted:
1911-07-05
Date accepted:
1911-09-29
Date published:
1912-01-01

Abstract

When expanding “arbitrary” functions into series using the method of least squares, the coefficients of the series, as is known, are formed according to a precisely defined law. Specifically, the law of formation of the coefficient is the same that would take place in the case of uniform convergence of the series, i.e., in other words, the coefficients acquire the form of the so-called Fourier coefficients and the series will be the so-called Fourier series of the expandable function. (see the article).

Область исследования:
(Archived) Articles
Funding:

None

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References

  1. Stekloff. Sur la théorie des séries trigonométriques. Cracovie 1903.
  2. Fatou. Acta Mathematica. 1906, p. 350.
  3. Picard. Traité d’Analyse, t. 1, p. 283. (2 edition).
  4. Stekloff et Tamarkine. Problème des vibrations transversales d’une verge élastique homogène. Rendiconti del Circolo Palermo. 1911 г.
  5. Stekloff. Sur la théorie de fermeture des systèmes de fonctions. 1911, p. 12.

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