On the theory of trigonometric series
Authors:
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 very specific law, namely, the law of formation of the coefficient is the one 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 functions, in the special case of expansion in trigonometric functions of the form (see article).
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(Archived) Articles
Funding:
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References
- Stekloff. Sur la théorie des séries trigonométriques. Cracovie 1903.
- Fatou. Acta Mathematica. 1906, стр. 350.
- Picard. Traité d’Analyse, t. 1, стр. 283. (2 edition).
- Stekloff et Tamarkine. Problème des vibrations transversales d’une verge élastique homogène. Rendiconti del Circolo Palermo. 1911 г.
- Stekloff. Sur la théorie de fermeture des systèmes de fonctions. 1911, p. 12.