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Length functions of lemniscates
Royal Institute of Technology, Stockholm, Sweden .
Volgograd State University, Russia .ORCID iD: 0000-0002-8422-6140
2003 (English)In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 112, no 4, 519-538 p.Article in journal (Refereed) Published
Abstract [en]

We study metric and analytic properties of generalized lemniscates Et(f)={z∈ℂ:ln|f(z)|=t}, where f is an analytic function. Our main result states that the length function |Et(f)| is a bilateral Laplace transform of a certain positive measure. In particular, the function ln|Et(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.

Place, publisher, year, edition, pages
Springer, 2003. Vol. 112, no 4, 519-538 p.
National Category
Mathematical Analysis
URN: urn:nbn:se:liu:diva-89274DOI: 10.1007/s00229-003-0411-3OAI: diva2:607600
Available from: 2013-02-25 Created: 2013-02-25 Last updated: 2014-10-08

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Tkachev, Vladimir
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