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On the Correctness of Finite-Rank Approximations by Series of Shifted Gaussians

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Abstract

In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite-rank approximations by linear systems. The main result for this approach is to establish correctness of the finite–rank linear system under consideration. And the main result of the paper is to prove correctness of the finite-rank linear system approximation. For that an explicit formula for the main determinant of the linear system is derived to demonstrate that it is non-zero.

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REFERENCES

  1. V. Mazya and G. Schmidt, Approximate Approximations, AMS Mathematical Surveys and Monographs (Am. Math. Soc., 2007).

  2. E. A. Kisilev, L. A. Minin, I. Ya. Novikov, and S. M. Sitnik, ‘‘On the Riesz constants for systems of integer translates,’’ Math. Notes 96, 228–238 (2014).

    Article  MathSciNet  Google Scholar 

  3. M. V. Zhuravlev, E. A. Kisilev, L. A. Minin, and S. M. Sitnik, ‘‘Jacobi theta-functions and systems of integer shifts of Gaussians,’’ Mod. Math. Appl. 67, 107–116 (2010).

    Google Scholar 

  4. S. M. Sitnik and A. S. Timashov, ‘‘Finite-rank mathematical model and its computation for the problem of quadratic exponential interpolation,’’ Vestn. Belgor. Univ., Mat. Fiz. 32, 184–186 (2013).

    Google Scholar 

  5. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis Cambridge Mathematical Library (Cambridge Univ. Press, 1996).

  6. V. V. Katrakhov and S. M. Sitnik, ‘‘The transmutation method and boundary-value problems for singular elliptic equations,’’ Contemp. Math. Fundam. Direct. 64, 211–426 (2018).

    Article  MathSciNet  Google Scholar 

  7. S. M. Sitnik and E. L. Shishkina, Method of Transmutations for Differential Equations with Bessel Operators (Fizmatlit, Moscow, 2019) [in Russian].

    Google Scholar 

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Correspondence to S. M. Sitnik, A. S. Timashov or S. N. Ushakov.

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(Submitted by A. M. Elizarov)

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Sitnik, S.M., Timashov, A.S. & Ushakov, S.N. On the Correctness of Finite-Rank Approximations by Series of Shifted Gaussians. Lobachevskii J Math 41, 423–429 (2020). https://doi.org/10.1134/S1995080220030166

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  • DOI: https://doi.org/10.1134/S1995080220030166

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