On two methods of determining $\eta$-invariants of elliptic boundary-value problems

K. N. Zhuikov, A. Yu. Savin

RUDN University, Moscow, Russia

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

Keywords: elliptic boundary-value problems with a parameter, $\eta$-invariants, spectral invariants, regularized traces.

UDC: 517.954

DOI: 10.22363/2413-3639-2024-70-3-403-416

 English version: Journal of Mathematical Sciences, 2024, 287:4, 587–600