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Operator representations of Herglotz-Nevanlinna functions in several variables

  • Erik Avelin
  • Mitja Nedic
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Abstract

In this paper, we present an operator representation for Herglotz-Nevanlinna functions in several variables using self-adjoint linear relations. Moreover, a description of the reproducing kernel Hilbert space corresponding to a Herglotz-Nevanlinna function of several variables is also presented, along with a comparison to some existing result concerning the class of Loewner functions.

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Cite

BibTeXRIS
BibTeX
@misc{avelin2026operator,
  title = {{Operator representations of Herglotz-Nevanlinna functions in several variables}},
  author = {Erik Avelin and Mitja Nedic},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04637},
  eprint = {2610.04637},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04637},
}
RIS
TY  - UNPB
TI  - Operator representations of Herglotz-Nevanlinna functions in several variables
AU  - Erik Avelin
AU  - Mitja Nedic
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04637
UR  - https://arxiv.org/abs/2610.04637
AB  - In this paper, we present an operator representation for Herglotz-Nevanlinna functions in several variables using self-adjoint linear relations. Moreover, a description of the reproducing kernel Hilbert space corresponding to a Herglotz-Nevanlinna function of several variables is also presented, along with a comparison to some existing result concerning the class of Loewner functions.
ER  -