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Entries of indefinite Nevanlinna matrices


Author: H. Woracek
Original publication: Algebra i Analiz, tom 26 (2014), nomer 5.
Journal: St. Petersburg Math. J. 26 (2015), 757-783
MSC (2010): Primary 46C20; Secondary 34B20, 30D10, 30D15
DOI: https://doi.org/10.1090/spmj/1357
Published electronically: July 27, 2015
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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.


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Additional Information

H. Woracek
Affiliation: Institut for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8–10/101, 1040 Wien, Austria
Email: harald.woracek@tuwien.ac.at

DOI: https://doi.org/10.1090/spmj/1357
Keywords: Nevanlinna matrix, Pontryagin space, entire function, Krein class
Received by editor(s): July 26, 2013
Published electronically: July 27, 2015
Additional Notes: The author gratefully acknowledges the support of the Austrian Science Fund (FWF), project I1536–N25, and the Russian Foundation for Basic Research (RFBR), project 13-01-91002-ANF
Article copyright: © Copyright 2015 American Mathematical Society