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Vector fields with a non-degenerate source

  • We discuss the solution theory of operators of the form del(x) + A, acting on smooth sections of a vector bundle with connection del over a manifold M, where X is a vector field having a critical point with positive linearization at some point p is an element of M. As an operator on a suitable space of smooth sections Gamma(infinity)(U, nu), it fulfills a Fredholm alternative, and the same is true for the adjoint operator. Furthermore, we show that the solutions depend smoothly on the data del, X and A.

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Author:Matthias Ludewig
ISSN:0393-0440 (print)
ISSN:1879-1662 (online)
Parent Title (English):Journal of geometry and physics
Place of publication:Amsterdam
Document Type:Article
Year of first Publication:2014
Year of Completion:2014
Release Date:2017/03/27
Tag:First order PDE; Fredholm alternative; Heat kernel coefficients; Recursive transport equations; Semiclassical analysis; WKB expansion
First Page:59
Last Page:76
Funder:Potsdam Graduate School (POGS)
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer Review:Referiert