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Vandermonde Operator and Bounded Solutions of Difference Equations

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We study the problem of the existence of a unique bounded solution of a linear difference equation of any order with bounded operator coefficients. The case where the corresponding “algebraic” operator equation has separated pairwise commuting roots is analyzed. By using the Vandermonde operator constructed on the basis of these roots, we obtain a representation of the unique bounded solution.

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Authors and Affiliations

  1. T. Shevchenko Kyiv National University, Volodymyrs’ka Str., 64, Kyiv, 01033, Ukraine

    M. F. Horodnii

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  1. M. F. Horodnii
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Correspondence to M. F. Horodnii.

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Translated from Neliniini Kolyvannya, Vol. 25, No. 2-3, pp. 184–190, April–September, 2022.

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Horodnii, M.F. Vandermonde Operator and Bounded Solutions of Difference Equations. J Math Sci 274, 833–840 (2023). https://doi.org/10.1007/s10958-023-06646-0

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