On the Loewner problem in the class
Authors:
D. Alpay, A. Dijksma and H. Langer
Journal:
Proc. Amer. Math. Soc. 130 (2002), 2057-2066
MSC (2000):
Primary 30E05, 47A57; Secondary 47B25, 47B50
DOI:
https://doi.org/10.1090/S0002-9939-01-06345-6
Published electronically:
December 31, 2001
MathSciNet review:
1896042
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Loewner's theorem on boundary interpolation of functions is proved under rather general conditions. In particular, the hypothesis of Alpay and Rovnyak (1999) that the function
, which is to be extended to an
function, is defined and continuously differentiable on a nonempty open subset of the real line, is replaced by the hypothesis that the set on which
is defined contains an accumulation point at which
satisfies some kind of differentiability condition. The proof of the theorem in this note uses the representation of
functions in terms of selfadjoint relations in Pontryagin spaces and the extension theory of symmetric relations in Pontryagin spaces.
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Additional Information
D. Alpay
Affiliation:
Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel
Email:
dany@math.bgu.ac.il
A. Dijksma
Affiliation:
Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands
Email:
dijksma@math.rug.nl
H. Langer
Affiliation:
Department of Mathematics, Technical University Vienna, Wiedner Hauptstrasse 8–10, A–1040 Vienna, Austria
Email:
hlanger@mail.zserv.tuwien.ac.at
DOI:
https://doi.org/10.1090/S0002-9939-01-06345-6
Received by editor(s):
October 26, 2000
Received by editor(s) in revised form:
February 9, 2001
Published electronically:
December 31, 2001
Additional Notes:
The second and third authors gratefully acknowledge support through Harry T. Dozor fellowships at the Ben-Gurion University of the Negev, Beer-Sheva, Israel, in the years 1999 and 2000 respectively, and support from NWO, the Netherlands Organization for Scientific Research (grant B 61-453).
Communicated by:
Juha M. Heinonen
Article copyright:
© Copyright 2001
American Mathematical Society