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Quasi-Herglotz functions and convex optimization
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.
Stockholm University.
Lund University.
KTH Royal Institute of Technology.
Show others and affiliations
2018 (English)Report (Other academic)
Abstract [en]

We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modeling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions, and we show that several of the important properties and modeling perspectives of Herglotz functions are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modeling of a non-passive gain media formulated as a convex optimization problem,where the generating measure is modeled by using a finite expansion of B-splines and point masses.

Place, publisher, year, edition, pages
2018. , p. 24
Keywords [en]
Quasi-Herglotz functions, non-passive systems, approximation, convex optimization, sum rules
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering Other Mathematics
Research subject
Physics, Waves and Signals
Identifiers
URN: urn:nbn:se:lnu:diva-78933OAI: oai:DiVA.org:lnu-78933DiVA, id: diva2:1265204
Funder
Swedish Foundation for Strategic Research , AM13-0011Available from: 2018-11-22 Created: 2018-11-22 Last updated: 2018-11-26Bibliographically approved

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Ivanenko, YevhenNordebo, Sven

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • 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