Length functions of lemniscates
| dc.creator | Kuznetsova, Olga | |
| dc.creator | Tkachev, Vladimir | |
| dc.date | 2003-06-23 | |
| dc.date | 2009-03-01 | |
| dc.date.accessioned | 2026-07-07T12:47:20Z | |
| dc.date.available | 2026-07-07T12:47:20Z | |
| dc.description | We study metric and analytic properties of generalized lemniscates E_t(f)={z:ln|f(z)|=t}, where f is an analytic function. Our main result states that the length function |E_t(f)| is a bilateral Laplace transform of a certain positive measure. In particular, the function ln|E_t(f)| is convex on any interval free of critical points of ln|f|. As another application we deduce explicit formulas of the length function in some special cases. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0306327 | |
| dc.identifier | http://arxiv.org/abs/math/0306327 | |
| dc.identifier | Manuscr. Math., 112(2003), no 4, 519-538 | |
| dc.identifier | doi:10.1007/s00229-003-0411-3 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221688 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.subject | 30E05; 42A82; 44A10 | |
| dc.title | Length functions of lemniscates | |
| dc.type | text |