Length functions of lemniscates

dc.creatorKuznetsova, Olga
dc.creatorTkachev, Vladimir
dc.date2003-06-23
dc.date2009-03-01
dc.date.accessioned2026-07-07T12:47:20Z
dc.date.available2026-07-07T12:47:20Z
dc.descriptionWe 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.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0306327
dc.identifierhttp://arxiv.org/abs/math/0306327
dc.identifierManuscr. Math., 112(2003), no 4, 519-538
dc.identifierdoi:10.1007/s00229-003-0411-3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221688
dc.subjectComplex Variables
dc.subjectDifferential Geometry
dc.subject30E05; 42A82; 44A10
dc.titleLength functions of lemniscates
dc.typetext

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