Operator Valued Dirichlet Problem in the Plane

Authors : Nihat Gökhan Göğüş

Pages : 269-280

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Publication Date : 2013-03-01

Article Type : Other Papers

Abstract :We consider an operator valued Dirichlet problem for harmonic mappings and prove the existence of a Perron-like solution. To formulatethe Perron’s construction we make use of Olson’s notion of spectralorder. We introduce a class of operator valued subharmonic mappingsand establish some of their elementary properties.
Keywords : Operator theory, Harmonic mappings, Perron method, Spectral order