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Pseudoconvexity and the envelope of holomorphy for functions of several complex variables

University of British Columbia

We first handle some generalizations from the theory of functions of a single complex variable, including results regarding analytic continuation. Several "theorems of continuity" are considered, along with the associated definitions of pseudoconvexity, and these are shown to be equivalent up to a special kind of transformation. By successively applying a form of analytic continuation to a function f , a set of pseudoconvex domains is constructed, and the union of these domains is shown to be the envelope of holomorphy of f .

Text

2011-08-31

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http://hdl.handle.net/2429/37041

Mathematics

University of British Columbia

Graduate