On quasi-Herglotz functions in one variable
In this paper, the class of (complex) quasi-Herglotz functions is introduced as the complex vector space generated by the convex cone of ordinary Herglotz functions. We prove characterization theorems, in particular, an analytic characterization. The subclasses of quasi-Herglotz functions that are i...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2022-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.364/ |
| _version_ | 1797651504717365248 |
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| author | Luger, Annemarie Nedic, Mitja |
| author_facet | Luger, Annemarie Nedic, Mitja |
| author_sort | Luger, Annemarie |
| collection | DOAJ |
| description | In this paper, the class of (complex) quasi-Herglotz functions is introduced as the complex vector space generated by the convex cone of ordinary Herglotz functions. We prove characterization theorems, in particular, an analytic characterization. The subclasses of quasi-Herglotz functions that are identically zero in one half-plane as well as rational quasi-Herglotz functions are investigated in detail. Moreover, we relate to other areas such as weighted Hardy spaces, definitizable functions, the Cauchy transform on the unit circle, sum-rule identities and matrix-valued Herglotz functions. |
| first_indexed | 2024-03-11T16:16:45Z |
| format | Article |
| id | doaj.art-e449eb7c5ac24c07b1ce6cc1ceb62980 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:45Z |
| publishDate | 2022-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-e449eb7c5ac24c07b1ce6cc1ceb629802023-10-24T14:19:34ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692022-09-01360G993797010.5802/crmath.36410.5802/crmath.364On quasi-Herglotz functions in one variableLuger, Annemarie0Nedic, Mitja1https://orcid.org/0000-0001-7867-5874Department of Mathematics, Stockholm University, SE-106 91 Stockholm, SwedenDepartment of Mathematics, Stockholm University, SE-106 91 Stockholm, SwedenIn this paper, the class of (complex) quasi-Herglotz functions is introduced as the complex vector space generated by the convex cone of ordinary Herglotz functions. We prove characterization theorems, in particular, an analytic characterization. The subclasses of quasi-Herglotz functions that are identically zero in one half-plane as well as rational quasi-Herglotz functions are investigated in detail. Moreover, we relate to other areas such as weighted Hardy spaces, definitizable functions, the Cauchy transform on the unit circle, sum-rule identities and matrix-valued Herglotz functions.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.364/ |
| spellingShingle | Luger, Annemarie Nedic, Mitja On quasi-Herglotz functions in one variable Comptes Rendus. Mathématique |
| title | On quasi-Herglotz functions in one variable |
| title_full | On quasi-Herglotz functions in one variable |
| title_fullStr | On quasi-Herglotz functions in one variable |
| title_full_unstemmed | On quasi-Herglotz functions in one variable |
| title_short | On quasi-Herglotz functions in one variable |
| title_sort | on quasi herglotz functions in one variable |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.364/ |
| work_keys_str_mv | AT lugerannemarie onquasiherglotzfunctionsinonevariable AT nedicmitja onquasiherglotzfunctionsinonevariable |