Eta-Invariants for Parameter-Dependent Operators Associated with an Action of a Discrete Group

被引：0
|
作者：
Zhuikov, K. N. [1 ]
Savin, A. Yu. [1 ]
机构：
[1] RUDN Univ, Peoples Friendship Univ Russia, Moscow 117198, Russia
来源：
MATHEMATICAL NOTES | 2022年 / 112卷 / 5-6期
关键词：
elliptic operator; parameter-dependent operator; nonlocal operator; -invariant; FAMILIES;
D O I：
10.1134/S0001434622110062
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：685 / 696
页数：12
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