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The best approximation of the differentiation operator in the metric of Lp

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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.

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Literature cited

  1. S. B. Stechkin, “The best approximation of linear operators,” Matem. Zametki,1, No. 2, 137–148 (1967).

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  2. N. Danford and D. Schwartz, Linear Operators, General Theory [Russian translation], Moscow (1962).

  3. V. V. Arestov, “The best uniform approximation of differentiation operators,” Matem. Zametki,5, No. 3, 273–284 (1969).

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  4. V. V. Arestov,“The best approximation of differentiation operators in a uniform metric,” Author's Abstract of Candidate's Dissertation, Moscow (1969).

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Academy of Sciences of the USSR, USSR

    V. N. Gabushin

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  1. V. N. Gabushin
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Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 531–538, November, 1972.

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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

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  • DOI: https://doi.org/10.1007/BF01099059

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