Quasi-Herglotz functions and convex optimization
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 functi...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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The Royal Society
2020-01-01
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| Series: | Royal Society Open Science |
| Subjects: | |
| Online Access: | https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.191541 |
| _version_ | 1819111923767050240 |
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| author | Y. Ivanenko M. Nedic M. Gustafsson B. L. G. Jonsson A. Luger S. Nordebo |
| author_facet | Y. Ivanenko M. Nedic M. Gustafsson B. L. G. Jonsson A. Luger S. Nordebo |
| author_sort | Y. Ivanenko |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-22T04:05:20Z |
| format | Article |
| id | doaj.art-f31935026ce349f1b114246c2ee91d7d |
| institution | Directory Open Access Journal |
| issn | 2054-5703 |
| language | English |
| last_indexed | 2024-12-22T04:05:20Z |
| publishDate | 2020-01-01 |
| publisher | The Royal Society |
| record_format | Article |
| series | Royal Society Open Science |
| spelling | doaj.art-f31935026ce349f1b114246c2ee91d7d2022-12-21T18:39:39ZengThe Royal SocietyRoyal Society Open Science2054-57032020-01-017110.1098/rsos.191541191541Quasi-Herglotz functions and convex optimizationY. IvanenkoM. NedicM. GustafssonB. L. G. JonssonA. LugerS. NordeboWe 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.https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.191541quasi-herglotz functionsnon-passive systemsapproximationconvex optimizationsum rules |
| spellingShingle | Y. Ivanenko M. Nedic M. Gustafsson B. L. G. Jonsson A. Luger S. Nordebo Quasi-Herglotz functions and convex optimization Royal Society Open Science quasi-herglotz functions non-passive systems approximation convex optimization sum rules |
| title | Quasi-Herglotz functions and convex optimization |
| title_full | Quasi-Herglotz functions and convex optimization |
| title_fullStr | Quasi-Herglotz functions and convex optimization |
| title_full_unstemmed | Quasi-Herglotz functions and convex optimization |
| title_short | Quasi-Herglotz functions and convex optimization |
| title_sort | quasi herglotz functions and convex optimization |
| topic | quasi-herglotz functions non-passive systems approximation convex optimization sum rules |
| url | https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.191541 |
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