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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Local Dirichlet spaces
as de Branges-Rovnyak spaces


Author: Donald Sarason
Journal: Proc. Amer. Math. Soc. 125 (1997), 2133-2139
MSC (1991): Primary 46E20
MathSciNet review: 1396993
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Abstract: The harmonically weighted Dirichlet spaces associated with unit point masses are shown to coincide with de Branges-Rovnyak spaces, with equality of norms. As a consequence it is shown that radial expansion operators act contractively in harmonically weighted Dirichlet spaces.


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Additional Information

Donald Sarason
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: sarason@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03896-3
PII: S 0002-9939(97)03896-3
Received by editor(s): February 13, 1996
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society