Elliptic G-Operators on Manifolds with Isolated Singularities
- 9 Downloads
In the present work we study elliptic operators on manifolds with singularities in the situation where the manifold is endowed with an action of a discrete group G. As usual in elliptic theory, the Fredholm property of an operator is governed by the properties of its principal symbol. We show that the principal symbol in our situation is a pair consisting of the symbol on the main stratum (interior symbol) and the symbol at the conical point (conormal symbol). The Fredholm property of elliptic elements is obtained.
Unable to display preview. Download preview PDF.
- 7.V. Nazaikinskii, A. Savin, and B. Sternin, “Elliptic theory on manifolds with corners. I. Dual manifolds and pseudodifferential operators,” In: C*-algebras and Elliptic Theory. II, 183–206, Birkhäuser, Basel (2008).Google Scholar
- 12.A. Savin and B. Sternin, “Elliptic theory for operators associated with diffeomorphisms of smooth manifolds,” In: Pseudo-Differential Operators, Generalized Functions and Asymptotics, Birkhäuser (2013), pp. 1–26.Google Scholar
- 14.B. Sternin, Elliptic Operators on Manifolds with Singularities [in Russian], Moscow Inst. Electron. Engineering, Moscow (1972).Google Scholar
- 15.B. Sternin, Quasielliptic Equations on an Infinite Cylinder [in Russian], Moscow Inst. Electron. Engineering, Moscow (1972).Google Scholar