eta-INVARIANT AND INDEX FOR OPERATORS ON THE REAL LINE PERIODIC AT INFINITY

We define eta-invariants for periodic pseudodifferential operators on the real line and establish their main properties. In particular, it is proved that the eta-invariant satisfies logarithmic property and a formula for the derivative of the eta-invariant of an operator family with respect to the parameter is obtained. Furthermore, we establish an index formula for elliptic pseudodifferential operators on the real line periodic at infinity. The contribution of infinity to the index formula is given by the constructed n-invariant. Finally, we compute eta-invariants of differential operators in terms of the spectrum of their monodromy matrices.

Authors
Publisher
Eurasian Mathematical Journal
Number of issue
3
Language
English
Pages
57-77
Status
Published
Volume
12
Year
2021
Organizations
  • 1 Peoples Friendship Univ Russia, RUDN Univ, SM Nikolskii Math Inst, 6 Miklukho Maklaya St, Moscow 117198, Russia
  • 2 Leibniz Univ Hannover, Inst Anal, Welfengarten 1, D-30167 Hannover, Germany
Keywords
elliptic operator; operator with periodic coefficients; eta-invariant; index
Date of creation
16.12.2021
Date of change
16.12.2021
Short link
https://repository.rudn.ru/en/records/article/record/77520/
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