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Local Dirichlet spaces as de Branges-Rovnyak spaces
Author(s):
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.
References:
- 1.
- L. de Branges and J. Rovnyak, Square Summable Power Series, Holt, Rinehart, and Winston, New York, 1966. MR 35:5909
- 2.
- B. A. Lotto and D. Sarason, Multipliers of de Branges-Rovnyak spaces, Indiana Univ. Math. J. 42 (1993), 907-920. MR 95a:46039
- 3.
- S. Richter, A representation theorem for cyclic analytic two-isometries, Trans. Amer. Math. Soc. 328 (1991), 325-349. MR 92e:47052
- 4.
- S. Richter and C. Sundberg, A formula for the local Dirichlet integral, Michigan Math. J. 38 (1991), 355-379. MR 92i:47035
- 5.
- S. Richter and C. Sundberg, Multipliers and invariant subspaces in the Dirichlet space, J. Operator Theory 28 (1992), 167-186. MR 95e:47007
- 6.
- S. Richter and C. Sundberg, Invariant subspaces of the Dirichlet shift and pseudocontinuations, Trans. Amer. Math. Soc. 341 (1994), 863-879. MR 94d:47026
- 7.
- D. Sarason, Sub-Hardy Hilbert Spaces in the Unit Disk, Wiley, New York, 1995.
- 8.
- D. Sarason, Harmonically weighted Dirichlet spaces associated with finitely atomic measures, in preparation.
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Additional Information:
Donald
Sarason
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
Email:
sarason@math.berkeley.edu
DOI:
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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