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This article is cited in 1 scientific paper (total in 1 paper)
Eta-invariant of elliptic parameter-dependent boundary-value problems
K. N. Zhuikov, A. Yu. Savin RUDN University, Moscow, Russia
Abstract:
In this paper, we study the eta-invariant of elliptic parameter-dependent boundary value problems and its main properties. Using Melrose's approach, we define the eta-invariant as a regularization of the winding number of the family. In this case, the regularization of the trace requires obtaining the asymptotics of the trace of compositions of invertible parameter-dependent boundary value problems for large values of the parameter. Obtaining the asymptotics uses the apparatus of pseudodifferential boundary value problems and is based on the reduction of parameter-dependent boundary value problems to boundary value problems with no parameter.
Keywords:
eta-invariant, elliptic parameter-dependent boundary value problem, pseudodifferential boundary value problem, Boutet de Monvel operator, regularized trace.
Citation:
K. N. Zhuikov, A. Yu. Savin, “Eta-invariant of elliptic parameter-dependent boundary-value problems”, CMFD, 69, no. 4, PFUR, M., 2023, 599–620
Linking options:
https://www.mathnet.ru/eng/cmfd517 https://www.mathnet.ru/eng/cmfd/v69/i4/p599
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Abstract page: | 92 | Full-text PDF : | 21 | References: | 10 |
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