2016/12/09 by A. Savin, Anton Savin, Elmar Schrohe +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebra over a field #Elliptic operator #Elliptic rational functions #Group (periodic table) #Holomorphic and Operator Theory #Manifold (fluid mechanics) #Operator theory #Property (philosophy) #Pseudodifferential operators #math.AP #math.OA #msc:35S30 #msc:46L89 #msc:58J05 #msc:58J40
paper · pdf · doi:10.1016/j.bulsci.2019.01.010
published as Bull. Sci. Math. 155 (2019) 141-167 · 23 pages
arxiv created 2016/12/09 · openalex created_date 2017/01/06 · openalex publication_date 2019/01/24 · arxiv updated 2020/08/04 · openalex updated_date 2026/08/05
Given a Lie group G of quantized canonical transformations acting on the space L2(M) over a closed manifold M, we define an algebra of so-called G-operators on L2(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.