Submit an Article
Become a reviewer
Vol 6 Iss. 1
Pages:
10-14
Download volume:
RUS
Article

On some inequalities established in the exposition of the Schwartz-Poincare — Steklov method and also encountered in solving many minimal problems

Authors:
N. M. Krylov
Date submitted:
1916-06-30
Date accepted:
1916-08-14
Date published:
1916-12-01

Abstract

In various mathematical studies related to the question of the existence of a minimum, it is often useful, as we shall attempt to show below, to apply that fundamental relation in the theory of trigonometric series which was named by Prof. V. A. Steklov the "closure equation" and generalized by him to many other systems of orthogonal functions encountered in analysis and mathematical physics.

Область исследования:
(Archived) Articles
Funding:

None

Go to volume 6

References

  1. Steklov. Problem of the Cooling of a Heterogeneous Bar. Annales de la Faculté des Sciences de Toulouse, 2nd series, vol. III.
  2. Hadamard. Calculus of Variations, p. 335.
  3. Tamarkin. Applications of the Method of Fundamental Functions. (Communications of the Kharkov Mathematical Society, 1910).
  4. Zapiski Gornogo Instituta. Vol. IV, issue VI. "On the Closure Theorem in the Theory of Trigonometric Series." (in Russian)
  5. Comptes Rendus. 1902. September 10.
  6. Annali di Matematica, Vol. 12, series III.

Similar articles

On the remainder term of the Lagrange interpolation formula
1916 N. M. Krylov
A note on the remainder term of the Taylor series
1916 N. M. Krylov
The triplicity of the orientation of trigonaloid crystals
1916 E. S. Fedorov
On the variational methods of Ritz and Boussinesq
1916 N. M. Krylov
A theorem analogous to Pascal's theorem, but relating to space
1916 E. S. Fedorov
On singular Abelian functions
1916 N. V. Lipin