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An example of a complete orthonormal system in a Hilbert space of generalized functions

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Abstract

We construct a complete orthonormal system of generalized functions in a Hilbert space W −1. We obtain an estimate of the error of approximation in W −1, which is expressed in terms of the integral modulus of continuity of a function from L 2.

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References

  1. V. P. Didenko and I. I. Lyashko, Dynamical Systems with Discontinuous Characteristics [in Russian]] Kiev University, Kiev (1977).

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  2. N. P. Korneichuk, Extremal Problems in the Theory of Approximations [in Russian], Nauka, Moscow (1976).

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  3. O. V. Gladkivs’ka, Investigation of Identification Problems for a Class of Dynamical Models [in Russian], Author’s Abstract of the Candidate Degree Thesis (Physics and Mathematics), Kiev (1990).

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Authors
  1. O. V. Gladkivs’ka
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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 725–728, May, 1997.

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Gladkivs’ka, O.V. An example of a complete orthonormal system in a Hilbert space of generalized functions. Ukr Math J 49, 812–815 (1997). https://doi.org/10.1007/BF02486463

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  • DOI: https://doi.org/10.1007/BF02486463

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