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.
Author details: | Matthias Ludewig |
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DOI: | https://doi.org/10.1016/j.geomphys.2014.01.014 |
ISSN: | 0393-0440 |
ISSN: | 1879-1662 |
Title of parent work (English): | Journal of geometry and physics |
Publisher: | Elsevier |
Place of publishing: | Amsterdam |
Publication type: | Article |
Language: | English |
Year of first publication: | 2014 |
Publication year: | 2014 |
Release date: | 2017/03/27 |
Tag: | First order PDE; Fredholm alternative; Heat kernel coefficients; Recursive transport equations; Semiclassical analysis; WKB expansion |
Volume: | 79 |
Number of pages: | 18 |
First page: | 59 |
Last Page: | 76 |
Funding institution: | Potsdam Graduate School (POGS) |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |