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On interpolation approximation of differentiable operators in a Hilbert space

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Abstract

In a Hilbert space, we construct an interpolation approximation of the Taylor polynomial for differentiable operators. By using this approximation, we obtain estimates of accuracy for analytic operators that strengthen previously known results and for operators containing finitely many Fréchet derivatives.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    V. V. Khlobystov

  2. Shevchenko Kiev National University, Kiev

    T. N. Popovicheva

Authors
  1. V. V. Khlobystov
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  2. T. N. Popovicheva
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 4, pp. 554–563, April, 2006.

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Khlobystov, V.V., Popovicheva, T.N. On interpolation approximation of differentiable operators in a Hilbert space. Ukr Math J 58, 630–639 (2006). https://doi.org/10.1007/s11253-006-0088-3

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  • DOI: https://doi.org/10.1007/s11253-006-0088-3

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