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

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. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.