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Elliptic theory for operators associated with diffeomorphisms of smooth manifolds. (English) Zbl 1269.58009
Molahajloo, Shahla (ed.) et al., Pseudo-differential operators, generalized functions and asymptotics. Selected papers of the 8th ISAAC congress, Moscow, Russia, August 22–27, 2011. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0584-1/hbk; 978-3-0348-0585-8/ebook). Operator Theory: Advances and Applications 231, 1-26 (2013).
Summary: In this paper, we give a survey of elliptic theory for operators associated with diffeomorphisms of smooth manifolds. Such operators appear naturally in analysis, geometry and mathematical physics. We survey classical results as well as results obtained recently. The paper consists of an introduction and three sections. In the introduction, we give a general overview of the area of research. For the reader’s convenience, here we tried to keep special terminology to a minimum. In the remaining sections we give detailed formulations of the most important results mentioned in the introduction.
For the entire collection see [Zbl 1260.00029].

##### MSC:
 58J20 Index theory and related fixed-point theorems on manifolds 58J28 Eta-invariants, Chern-Simons invariants 58J32 Boundary value problems on manifolds 19K56 Index theory 46L80 $$K$$-theory and operator algebras (including cyclic theory) 58J22 Exotic index theories on manifolds 57S05 Topological properties of groups of homeomorphisms or diffeomorphisms 58-02 Research exposition (monographs, survey articles) pertaining to global analysis 58J40 Pseudodifferential and Fourier integral operators on manifolds
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