On some inequalities established in the exposition of the Schwartz-Poincare — Steklov method and also encountered in solving many minimal problems
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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.
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References
- Steklov. Problem of the Cooling of a Heterogeneous Bar. Annales de la Faculté des Sciences de Toulouse, 2nd series, vol. III.
- Hadamard. Calculus of Variations, p. 335.
- Tamarkin. Applications of the Method of Fundamental Functions. (Communications of the Kharkov Mathematical Society, 1910).
- Zapiski Gornogo Instituta. Vol. IV, issue VI. "On the Closure Theorem in the Theory of Trigonometric Series." (in Russian)
- Comptes Rendus. 1902. September 10.
- Annali di Matematica, Vol. 12, series III.