Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



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
Published electronically: July 27, 2015
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 46C20, 34B20, 30D10, 30D15

Retrieve articles in all journals with MSC (2010): 46C20, 34B20, 30D10, 30D15

Additional Information

H. Woracek
Affiliation: Institut for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8–10/101, 1040 Wien, Austria

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

American Mathematical Society