Abstract
We derive an analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function. Here, the main tools used are the so-called variable non-dependence property and the symmetry formula satisfied by Herglotz-Nevanlinna and Cauchy-type functions. We also provide an extension of the Stieltjes inversion formula for Cauchy-type and quasi-Cauchy-type functions.
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Acknowledgements
The author would like to thank Dale Frymark for many enthusiastic discussions on the subject. The author would also like to thank the anonymous referee for suggesting to expand the article with a section on complex measures.
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Open access funding provided by University of Helsinki.
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Nedic, M. An analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function. Czech Math J 73, 117–134 (2023). https://doi.org/10.21136/CMJ.2022.0455-21
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DOI: https://doi.org/10.21136/CMJ.2022.0455-21
Keywords
- Herglotz-Nevanlinna function
- Cauchy-type function
- symmetric extension
- Stieltjes inversion formula
MSC 2020
- 32A36
- 32A99