Abstract
For Stechkin's problem of the best approximation for the differentiation operator
we indicate the necessary and sufficient conditions that En be finite. We study some properties of continuous linear operators V from Lp into Lq.
Similar content being viewed by others
Literature cited
S. B. Stechkin, “The best approximation of linear operators,” Matem. Zametki,1, No. 2, 137–148 (1967).
N. Danford and D. Schwartz, Linear Operators, General Theory [Russian translation], Moscow (1962).
V. V. Arestov, “The best uniform approximation of differentiation operators,” Matem. Zametki,5, No. 3, 273–284 (1969).
V. V. Arestov,“The best approximation of differentiation operators in a uniform metric,” Author's Abstract of Candidate's Dissertation, Moscow (1969).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 531–538, November, 1972.
Rights and permissions
About this article
Cite this article
Gabushin, V.N. The best approximation of the differentiation operator in the metric of Lp . Mathematical Notes of the Academy of Sciences of the USSR 12, 756–760 (1972). https://doi.org/10.1007/BF01099059
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01099059