Local Dirichlet spaces as de Branges-Rovnyak spaces

Sarason, Donald

doi:10.1090/S0002-9939-97-03896-3

Local Dirichlet spaces as de Branges-Rovnyak spaces
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Proc. Amer. Math. Soc. 125 (1997), 2133-2139 Request permission

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

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