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Quasi-Herglotz functions and convex optimization
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.ORCID iD: 0000-0002-3928-6064
Stockholm University, Sweden.ORCID iD: 0000-0001-7867-5874
Lund University, Sweden.ORCID iD: 0000-0003-4362-5716
KTH Royal institute of technology, Sweden.ORCID iD: 0000-0001-7269-5241
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2020 (English)In: Royal Society Open Science, E-ISSN 2054-5703, Vol. 7, no 1, p. 1-15, article id 191541Article in journal (Refereed) Published
Abstract [en]

We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modelling 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 modelling perspectives 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 modelling of a non-passive gain medium formulated as a convex optimization problem, where the generating measure is modelled by using a finite expansion of B-splines and point masses.

Place, publisher, year, edition, pages
The Royal Society Publishing , 2020. Vol. 7, no 1, p. 1-15, article id 191541
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-90928DOI: 10.1098/rsos.191541ISI: 000507305300001OAI: oai:DiVA.org:lnu-90928DiVA, id: diva2:1385808
Funder
Swedish Foundation for Strategic Research , AM13-0011Available from: 2020-01-15 Created: 2020-01-15 Last updated: 2020-02-04Bibliographically approved

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Ivanenko, YevhenNedic, MitjaGustafsson, MatsJonsson, B. L. G.Nordebo, Sven
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