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<p>We solve the problem of perturbation of the spectrum of a linear operator by a linear operator using the introduced concepts of holomorphic families of operators of type (A) and in the sense of Kato. The Rayleigh–Schrödinger series constructed in this case already were convergent in the usual sense but not asymptotically. In this work, we find the conditions for holomorphy of eigenpairs with respect to a small parameter in the case where a linear operator is perturbed by a nonlinear operator generated by a product in a Banach algebra.</p>

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ON ONE NONLINEAR SPECTRAL PROBLEM

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • V. I. Kachalov

摘要

We solve the problem of perturbation of the spectrum of a linear operator by a linear operator using the introduced concepts of holomorphic families of operators of type (A) and in the sense of Kato. The Rayleigh–Schrödinger series constructed in this case already were convergent in the usual sense but not asymptotically. In this work, we find the conditions for holomorphy of eigenpairs with respect to a small parameter in the case where a linear operator is perturbed by a nonlinear operator generated by a product in a Banach algebra.