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On the optimal reconstruction of the values of operators

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Abstract

For a continuous operatorA∶X → Y, we formulate the problem of optimal reconstruction of its valuesAx, x εX, by decreasing the domain of uncertainty ofAx in the spaceY by collecting additional informationμ k (x),k=1,2,..., whereμ k are continuous functionals given in the spaceX. Explicit results are obtained for some integral operators in functional spaces.

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References

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Authors and Affiliations

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

    N. P. Korneichuk (Corresponding Member)

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  1. N. P. Korneichuk
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1375–1381, October, 1994.

This work was supported by the Foundation for Fundamental Researches of the Ukrainian State Committee on Science and Technology.

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Korneichuk, N.P. On the optimal reconstruction of the values of operators. Ukr Math J 46, 1519–1526 (1994). https://doi.org/10.1007/BF01066095

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  • DOI: https://doi.org/10.1007/BF01066095

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