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Small Time Asymptotics on the Diagonal for Hörmander’s Type Hypoelliptic Operators
| Content Provider | Semantic Scholar |
|---|---|
| Author | Paoli, Elisa Antares |
| Copyright Year | 2015 |
| Abstract | We compute the small time asymptotics of the fundamental solution of Hörmander’s type hypoelliptic operators with drift, on the diagonal at a point x0. We show that the order of the asymptotics depends on the controllability of an associated control problem and of its approximating system. If the control problem of the approximating system is controllable at x0, then so is also the original control problem, and in this case we show that the fundamental solution blows up as t−N/2$\phantom {\dot {i}\!}t^{-\mathcal {N}/2}$, where N$\phantom {\dot {i}\!}\mathcal {N}$ is a number determined by the Lie algebra at x0 of the fields, that define the hypoelliptic operator. |
| Starting Page | 111 |
| Ending Page | 143 |
| Page Count | 33 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s10883-016-9321-z |
| Volume Number | 23 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1502.06361v2.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s10883-016-9321-z |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
