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1. On the Algebra of Operators Corresponding to the Union of Smooth Submanifolds

Author

D. A. Poluektova, A. Yu. Savin, and B. Yu. Sternin

Subjects
Statistics and Probability, Pseudodifferential operators, Applied Mathematics, General Mathematics, Boundary (topology), General Medicine, Composition (combinatorics), Manifold, Algebra, Mathematics::Differential Geometry, Algebra over a field, Mathematics::Symplectic Geometry, Symbol (formal), Mathematics
Abstract

For a pair of smooth transversally intersecting submanifolds in some enveloping smooth manifold, we study the algebra generated by pseudodifferential operators and (co)boundary operators corresponding to submanifolds. We establish that such an algebra has 18 types of generating elements. For operators from this algebra, we define the concept of symbol and obtain the composition formula.

Published
2022

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