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Operator representations of Herglotz-Nevanlinna functions in several variables

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Erik Avelin, Mitja Nedic

Functional Analysis · Submitted 3 Oct 2026

abstract compiled · 2026-10-06 · no language-model review

The authors' main claim In this paper, we present an operator representation for Herglotz-Nevanlinna functions in several variables using self-adjoint linear relations.

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arXiv ID2610.04637 (version 1)
Pith ID3RTFHJHN, Pith's permanent record of this paper and its review
CitationErik Avelin, Mitja Nedic. "Operator representations of Herglotz-Nevanlinna functions in several variables." arXiv:2610.04637 (2026). https://pith.science/paper/3RTFHJHN
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-06: 1 request, 2,329 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.05 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper, we present an operator representation for Herglotz-Nevanlinna functions in several variables using self-adjoint linear relations. contribution 0.99 0.95 0.82 asserted 1.00
s1 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. contribution 0.98 0.89 0.15 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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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