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manuscripta mathematica

, Volume 112, Issue 4, pp 519–538 | Cite as

Length functions of lemniscates

  • O.S. Kuznetsova
  • V.G. TkachevEmail author
Article

Abstract.

We study metric and analytic properties of generalized lemniscates E t (f)={z∈ℂ: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 formulae of the length function in some special cases.

Keywords

Analytic Function Result State Explicit Formula Analytic Property Positive Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Royal Institute of TechnologyStockholmSweden
  2. 2.Volgograd State UniversityVolgogradRussia

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