Complete Nevanlinna-Pick property of Dirichlet-type spaces

By S. Shimorin. 2002

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We prove that all Dirichlet-type spaces of functions analytic in the unit disk whose derivatives are square area integrable with superharmonic weights have complete Nevanlinna-Pick reproducing kernels. As a corollary, we obtain a commutant lifting theorem for cyclic analytic two-isometries. (C) 2002 Elsevier Science (USA).

Subfields: Applied Mathematics

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