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Quasi-Herglotz functions and convex optimization

Ivanenko, Y. LU ; Nedic, M. ; Gustafsson, M. LU orcid ; Jonsson, B. L.G. ; Luger, A. LU and Nordebo, S. LU (2020) In Royal Society Open Science 7(1).
Abstract

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... (More)

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.

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author
; ; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Approximation, Convex optimization, Non-passive systems, Quasi-Herglotz functions, Sum rules
in
Royal Society Open Science
volume
7
issue
1
article number
191541
publisher
Royal Society Publishing
external identifiers
  • pmid:32218971
  • scopus:85079589957
ISSN
2054-5703
DOI
10.1098/rsos.191541
language
English
LU publication?
yes
id
d70e873e-e2ad-464a-958c-2693c271429e
date added to LUP
2020-03-04 14:15:25
date last changed
2024-04-03 02:04:07
@article{d70e873e-e2ad-464a-958c-2693c271429e,
  abstract     = {{<p>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.</p>}},
  author       = {{Ivanenko, Y. and Nedic, M. and Gustafsson, M. and Jonsson, B. L.G. and Luger, A. and Nordebo, S.}},
  issn         = {{2054-5703}},
  keywords     = {{Approximation; Convex optimization; Non-passive systems; Quasi-Herglotz functions; Sum rules}},
  language     = {{eng}},
  month        = {{01}},
  number       = {{1}},
  publisher    = {{Royal Society Publishing}},
  series       = {{Royal Society Open Science}},
  title        = {{Quasi-Herglotz functions and convex optimization}},
  url          = {{http://dx.doi.org/10.1098/rsos.191541}},
  doi          = {{10.1098/rsos.191541}},
  volume       = {{7}},
  year         = {{2020}},
}