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<p>We consider two spectral problems for a fourth-order differential equation. Namely, the corresponding fourth-order differential operator is perturbed by a second-order operator with an absolutely continuous coefficient on a unit interval. At the same time, one or two boundary conditions contain a spectral parameter. We obtain regularized trace formulas for these problems.</p>

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Trace Formula for a Fourth-Order Differential Equation with a Spectral Parameter in the Boundary Conditions

  • 期刊论文

  • 发表日期：

    2026年6月2日

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  • Dmitry M. Polyakov

摘要

We consider two spectral problems for a fourth-order differential equation. Namely, the corresponding fourth-order differential operator is perturbed by a second-order operator with an absolutely continuous coefficient on a unit interval. At the same time, one or two boundary conditions contain a spectral parameter. We obtain regularized trace formulas for these problems.