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Algebra i Analiz, 2014, Volume 26, Issue 5, Pages 88–124 (Mi aa1398)  
Research Papers

Entries of indefinite Nevanlinna matrices

H. Woracek

Institut for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße, 8--10/101, 1040, Wien, Austria
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Abstract: In the early 1950's, M. G. Krein characterized the entire functions that are an entry of some Nevanlinna matrix, and the pairs of entire functions that are a row of some Nevanlinna matrix. In connection with Pontryagin space versions of Krein's theory of entire operators and de Branges' theory of Hilbert spaces of entire functions, an indefinite analog of the Nevanlinna matrices plays a role. In the paper, the above-mentioned characterizations are extended to the indefinite situation and the geometry of the associated reproducing kernel Pontryagin spaces is investigated.
Keywords: Nevanlinna matrix, Pontryagin space, entire function, Krein class.
Received: 26.07.2013
English version:
St. Petersburg Mathematical Journal, 2015, Volume 26, Issue 5, Pages 757–783
DOI: https://doi.org/10.1090/spmj/1357
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Document Type: Article
Language: English
Citation: H. Woracek, “Entries of indefinite Nevanlinna matrices”, Algebra i Analiz, 26:5 (2014), 88–124; St. Petersburg Math. J., 26:5 (2015), 757–783
Citation in format AMSBIB
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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