Quasi-Herglotz functions and convex optimization
(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
- Ivanenko, Y. LU ; Nedic, M. ; Gustafsson, M. LU ; Jonsson, B. L.G. ; Luger, A. LU and Nordebo, S. LU
- organization
- publishing date
- 2020-01-15
- 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
- 2024-08-21 17:53:53
@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}}, }