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 |
|---|---|
| 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 |
