Submit an Article
Become a reviewer
Vol 4 Iss. 1
Pages:
54-62
Download volume:
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 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).

Область исследования:
(Archived) Articles
Go to volume 4

References

  1. Stekloff. Sur la théorie des séries trigonométriques. Cracovie 1903.
  2. Fatou. Acta Mathematica. 1906, стр. 350.
  3. Picard. Traité d’Analyse, t. 1, стр. 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.

Similar articles

In memory of I. P. Dolbnya
1912 Volume 4(1)
List of works by Professor I. P. Dolbnya in chronological order of their appearance
1912 Volume 4(1)
On the integration of first order partial differential equations
1912 I. P. Dolbnya
Determining the most advantageous dimensions of a mine field
1912 L. M. Rutenberg
Deriving formulas for calculating the faces of the original belt using the zonal calculation system
1912 E. S. Fedorov
About the rocks of a small part of the gold-bearing area in the Semipalatinsk region
1912 G. G. Kell