Optimal control in Bombieri's and Tammi's conjectures
| dc.creator | Prokhorov, Dmitri | |
| dc.creator | Vasil'ev, Alexander | |
| dc.date | 2004-10-27 | |
| dc.date.accessioned | 2026-07-07T06:32:10Z | |
| dc.date.available | 2026-07-07T06:32:10Z | |
| dc.description | Let $S$ stand for the usual class of univalent regular functions in the unit disk $U=\{z: |z|<1\}$ normalized by $f(z)=z+a_2z^2+...$ in $U$, and let $S^M$ be its subclass defined by restricting $|f(z)|<M$ in $U$, $M\geq 1$. We consider two classical problems: Bombieri's coefficient problem for the class $S$ and the sharp estimate of the fourth coefficient of a function from $S^M$. Using Löwner's parametric representation and the optimal control method we give exact initial Bombieri's numbers and derive a sharp constant $M_0$, such that for all $M\geq M_0$ the Pick function gives the local maximum to $|a_4|$. Numerical approximation is given. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0410578 | |
| dc.identifier | http://arxiv.org/abs/math/0410578 | |
| dc.identifier | Georgian Math. J. 12 (2005), no. 4, 739-757 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98820 | |
| dc.subject | Complex Variables | |
| dc.subject | Optimization and Control | |
| dc.subject | 30C50; 49K15 | |
| dc.title | Optimal control in Bombieri's and Tammi's conjectures | |
| dc.type | text |