Operator Valued Dirichlet Problem in the Plane

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.

Operator Valued Dirichlet Problem in the Plane

Abstract

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Keywords

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References

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