Local Dirichlet spaces as de Branges-Rovnyak spaces

1997/01/01 by Donald Sarason · 11 citations
Mathematics · #Holomorphic and Operator Theory #Geometric Analysis and Curvature Flows #Advanced Harmonic Analysis Research

paper · pdf · doi:10.1090/s0002-9939-97-03896-3

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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