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On the exponential transform of lemniscates
Mathematical department, KTH, Stockholm, Sweden.
Mathematical department, KTH, Stockholm, Sweden .ORCID iD: 0000-0002-8422-6140
2011 (English)In: Notions of Positivity and the Geometry of Polynomials / [ed] P. Brändén, M. Passare and M. Putinar, Basel: Springer, 2011, 239-257 p.Chapter in book (Other academic)
Abstract [en]

It is known that the exponential transform of a quadrature domain is a rational function for which the denominator has a certain separable form. In the present paper we show that the exponential transform of lemniscate domains in general are not rational functions, of any form. Several examples are given to illustrate the general picture. The main tool used is that of polynomial and meromorphic resultants.

Place, publisher, year, edition, pages
Basel: Springer, 2011. 239-257 p.
Series
Trends in Mathematics
Keyword [en]
exponential transform; lemniscates; quadrature domain; resultant; Schwarz function; moment; Appell function
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-89269DOI: 10.1007/978-3-0348-0142-3_13ISBN: 978-3-0348-0141-6 (print)ISBN: 978-3-0348-0142-3 (electronic)OAI: oai:DiVA.org:liu-89269DiVA: diva2:607590
Available from: 2013-02-25 Created: 2013-02-25 Last updated: 2014-10-08Bibliographically approved

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Tkachev, Vladimir

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Mathematical Analysis

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf