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<p>For a class of parameter-dependent boundary-value problems that are elliptic in the sense of Agranovich–Vishik, we establish the equality of the <i>η</i>-invariant defined in terms of the Melrose regularization and the spectral <i>η</i>-invariant of the Atiyah–Patodi–Singer type defined using the analytic continuation of the spectral <i>η</i>-function of the operator.</p>

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On Two Methods of Determining η-Invariants of Elliptic Boundary-Value Problems

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • K. N. Zhuikov,
  • A. Yu. Savin

摘要

For a class of parameter-dependent boundary-value problems that are elliptic in the sense of Agranovich–Vishik, we establish the equality of the η-invariant defined in terms of the Melrose regularization and the spectral η-invariant of the Atiyah–Patodi–Singer type defined using the analytic continuation of the spectral η-function of the operator.