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The possibility of estimating the values of a function at given points of the measurement results of a finite number of its linear functionals

  • Theoretical and Mathematical Physics
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Moscow University Physics Bulletin Aims and scope

Abstract

The possibility of estimating the values of a function at given points of its domain is investigated. The estimation uses results of the measurements of a finite number of linear functionals; the results of the measurements are distorted by an error. It is shown that only the component of the functions from the linear finite-dimensional subspace can be estimated with a finite error. A method for estimating this component with accuracy control is proposed. The mathematical methods of measurement reduction proposed by Yu.P. Pyt’ev are used. An example of the estimation of an emission spectrum that is measured by a double-slit spectrometer is described.

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Authors and Affiliations

  1. Department of Physics, Moscow State University, Moscow, 119991, Russia

    A. I. Chulichkov & B. Yuan

Authors
  1. A. I. Chulichkov
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  2. B. Yuan
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Corresponding author

Correspondence to A. I. Chulichkov.

Additional information

Original Russian Text © A.I. Chulichkov, B. Yuan, 2014, published in Vestnik Moskovskogo Universiteta. Fizika, 2014, No. 3, pp. 15–19.

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Chulichkov, A.I., Yuan, B. The possibility of estimating the values of a function at given points of the measurement results of a finite number of its linear functionals. Moscow Univ. Phys. 69, 218–222 (2014). https://doi.org/10.3103/S0027134914030059

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  • DOI: https://doi.org/10.3103/S0027134914030059

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