Analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformations

We consider elliptic operators associated with discrete groups of quantized canonical transformations. In order to be able to apply results from algebraic index theory, we define the localized algebraic index of the complete symbol of an elliptic operator. With the help of a calculus of semiclassical quantized canonical transformations, a version of Egorov's theorem and a theorem on trace asymptotics for semiclassical Fourier integral operators we show that the localized analytic index and the localized algebraic index coincide. As a corollary, we express the Fredholm index in terms of the algebraic index for a wide class of groups, in particular, for finite extensions of Abelian groups. © 2019 Elsevier Inc.

Авторы
Издательство
Academic Press Inc.
Номер выпуска
5
Язык
Английский
Статус
Опубликовано
Номер
108400
Том
278
Год
2020
Организации
  • 1 Peoples' Friendship University of Russia (RUDN University), Russian Federation
  • 2 Leibniz Universität Hannover, Germany
Ключевые слова
Algebraic index; Elliptic operator; Fredholm index; Semiclassical Fourier integral operator
Дата создания
10.02.2020
Дата изменения
10.02.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/56505/