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International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii
May 25, 2015 12:05, Пленарные доклады, Moscow, Steklov Mathematical Institute of RAS
 


Approximation of the differentiation operator by bounded linear operators in the space $L_2$ on the half-line

V. V. Arestov

Ural Federal University
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MP4 742.7 Mb
MP4 188.4 Mb
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Adobe PDF 221.7 Kb
Adobe PDF 153.6 Kb

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V. V. Arestov
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Abstract: We will discuss Stechkin's problem on the best approximation of the differentiation operator of order $k$ on the class of $n$ times differentiable functions $(0\le k < n)$ by bounded linear operators in the spaces $L_p$ on the real line and on the half-line as well as the related problem on the optimal recovery of smooth functions given with a known error. A solution of Stechkin's problem will be given in the space $L_2(0,\infty)$ for $k = 1$ and $n = 2;$ this result was obtained jointly with M.A.Filatova.

Materials: presentation.pdf (221.7 Kb), abstract.pdf (153.6 Kb)

References
  1. S. B. Stechkin, “Nailuchshee priblizhenie lineinykh operatorov”, Mat. zametki, 1:2 (1967), 137–148  mathnet  zmath
  2. V. V. Arestov, “Priblizhenie neogranichennykh operatorov ogranichennymi i rodstvennye ekstremalnye zadachi”, Uspekhi mat. nauk, 51:6 (1996), 89–124  mathnet  crossref  mathscinet  zmath
  3. V. I. Berdyshev, “Nailuchshee priblizhenie v $L[0,\infty)$ operatora differentsirovaniya”, Mat. zametki, 9:5 (1971), 477–481  mathnet  zmath
  4. V. V. Arestov, M. A. Filatova, “Best approximation of the differentiation operator in the space $L_2$ on the semiaxis”, JAT, 187 (2014), 65–81  mathscinet  zmath


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