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

Proof of one Fuchs theorem
1912 M. N. Akimov
Speech given on April 8, 1912 at a meeting of the Council of the Mining Institute of Empress Catherine II
1912 A. V. Vasil'ev
Fragments of memories of I. P. Dolbnya
1912 E. E. Semashkevich
Deriving formulas for calculating the faces of the original belt using the zonal calculation system
1912 E. S. Fedorov
About the Laplace series
1912 N. M. Krylov
New case of probable identity of two substances described as two different
1912 E. S. Fedorov