Uniformization and index of elliptic operators associated with diffeomorphisms of a manifold

We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely, differential operators with shifts induced by the action of a (not necessarily periodic) isometric diffeomorphism. The key to the solution is the method of uniformization. To the nonlocal problem we assign a pseudodifferential operator, with the same index, acting on the sections of an infinite-dimensional vector bundle on a compact manifold. We then determine the index in terms of topological invariants of the symbol, using the Atiyah—Singer index theorem. © 2015, Pleiades Publishing, Ltd.

Авторы
Savin A. 1, 2 , Schrohe E.2 , Sternin B. 1, 2
Номер выпуска
3
Язык
Английский
Страницы
410-420
Статус
Опубликовано
Том
22
Год
2015
Организации
  • 1 Peoples’ Friendship University of Russia, Miklukho-Maklaya Str. 6, Moscow, 117198, Russian Federation
  • 2 Institut für Analysis Gottfried, Wilhelm Leibniz Universität, Hannover Welfengarten 1, Hannover, 30167, Germany
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/4546/
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