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<p>We study the problem of existence of a unique bounded solution to a linear differential equation of any order with bounded operator coefficients. We consider the case where the corresponding “algebraic” operator equation has multiple separated pairwise commuting roots. By using the generalized Vandermonde operator constructed with the help of these roots, we obtain a representation of the unique bounded solution.</p>

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Generalized Vandermonde Operator and Bounded Solutions of Differential Equations

  • 期刊论文

  • 发表日期：

    2025年10月28日

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  • Mykhailo Horodnii

摘要

We study the problem of existence of a unique bounded solution to a linear differential equation of any order with bounded operator coefficients. We consider the case where the corresponding “algebraic” operator equation has multiple separated pairwise commuting roots. By using the generalized Vandermonde operator constructed with the help of these roots, we obtain a representation of the unique bounded solution.