Quantization on manifolds with an embedded submanifold

Autor:	Bohlen, Karsten, Schulz, René
Rok vydání:	2017
Předmět:	Mathematics - Differential Geometry Mathematics - Operator Algebras Mathematics - Symplectic Geometry 58J05 58B34
Druh dokumentu:	Working Paper
Popis:	We investigate a quantization problem which asks for the construction of an algebra for relative elliptic problems of pseudodifferential type associated to smooth embeddings. Specifically, we study the problem for embeddings in the category of compact manifolds with corners. The construction of a calculus for elliptic problems is achieved using the theory of Fourier integral operators on Lie groupoids. We show that our calculus is closed under composition and furnishes a so-called noncommutative completion of the given embedding. A representation of the algebra is defined and the continuity of the operators in the algebra on suitable Sobolev spaces is established. Comment: 46 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1710.02294 Zobrazit plný text záznamu View this record from Arxiv