Traces of G-Operators Concentrated on Submanifolds
- 16 Downloads
We consider the traces on submanifolds of G-operators generated by pseudodifferential operators and operators of shift along the orbits of a discrete group G. Such operators arise in various problems in differential equations and mathematical physics, for example, in Sobolev problems. We show that the trace of a G-operator on a submanifold is the sum of a pseudodifferential operator on the submanifold and a G-operator concentrated on a sub-submanifold.
Unable to display preview. Download preview PDF.
- 4.Antonevich, A.B., Lineinye funktsional’nye uravneniya: Operatornyi podkhod (Linear Functional Equations: Operator Approach), Minsk: Universitetskoe, 1988.Google Scholar
- 8.Nazaikinskii, V.E., Savin, A.Yu., and Sternin, B.Yu., Elliptic theory and noncommutative geometry, in Operator Theory: Advances and Applications, Basel: Birkhäuser, 2008, Vol.183.Google Scholar
- 9.Savin, A. and Sternin, B., On Traces of Operators Associated with Compact Lie Group Actions, 2015. arXiv: 1612.02286.Google Scholar