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arXiv · 1612.02981

Elliptic Operators Associated with Groups of Quantized Canonical Transformations

Anton Savin·Elmar Schrohe·Boris Sternin
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Abstract

Given a Lie group $G$ of quantized canonical transformations acting on the space $L^2(M)$ over a closed manifold $M$, we define an algebra of so-called $G$-operators on $L^2(M)$. We show that to $G$-operators we can associate symbols in appropriate crossed products with $G$, introduce a notion of ellipticity and prove the Fredholm property for elliptic elements. This framework encompasses many known elliptic theories, for instance, shift operators associated with group actions on $M$, transversal elliptic theory, transversally elliptic pseudodifferential operators on foliations, and Fourier integral operators associated with coisotropic submanifolds.

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Anton Savin, Elmar Schrohe, Boris Sternin. 2016-12-09. Elliptic Operators Associated with Groups of Quantized Canonical Transformations. https://doi.org/10.1016/j.bulsci.2019.01.010

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