Geodesic
Eta-Invariants for Parameter-Dependent Operators Associated with an Action of a Discrete Group
Matematičeskie zametki, Tome 112 (2022) no. 5, pp. 705-717

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$\eta$-invariants for a class of parameter-dependent nonlocal operators associated with an isometric action of a discrete group of polynomial growth on a smooth closed manifold are studied. The $\eta$-invariant is defined as the regularization of the winding number. The formula for the variation of the $\eta$-invariant when the operator changes is obtained. The results are based on the study of asymptotic expansions of traces of parameter-dependent nonlocal operators.
Keywords: elliptic operator, parameter-dependent operator, nonlocal operator
Mots-clés : $\eta$-invariant. 
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     author = {K. N. Zhuikov and A. Yu. Savin},
     title = {Eta-Invariants for {Parameter-Dependent} {Operators} {Associated} with an {Action} of a {Discrete} {Group}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {705--717},
     publisher = {mathdoc},
     volume = {112},
     number = {5},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_5_a5/}
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K. N. Zhuikov; A. Yu. Savin. Eta-Invariants for Parameter-Dependent Operators Associated with an Action of a Discrete Group. Matematičeskie zametki, Tome 112 (2022) no. 5, pp. 705-717. http://geodesic.mathdoc.fr/item/MZM_2022_112_5_a5/