Transcription of Lecture notes on several complex variables - math.tamu.edu
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Math 650, fall 2007 Texas A&M UniversityLecture notes on several complexvariablesHarold P. BoasDraft of December 7, 2007 Contents1 Power series .. Integral representations .. Partial differential equations .. Geometry .. 32 Power Domain of convergence .. Characterization of domains of convergence .. Natural boundaries .. Summary .. 93 Real convexity .. Convexity with respect to a class of functions .. Polynomial convexity .. Linear and rational convexity .. Holomorphic convexity.
dimensional complex variety, while the zero set of a holomorphic function in C1 is a zero-dimensional variety (that is, a discrete set of points). There is a mismatch between the dimension of the domain and the dimension of the
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