This work departs from earlier treatments of the subject by emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and mapping theory. While due homage is paid to the more traditional algebraic theory (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment.
Steven G. Krantz is an accomplished mathematician and an award-winning author. He has published more than 150 research articles and over 50 books. He has worked as an editor of several book series, research journals, and for the Notices of the AMS.
An introduction to the subject Some integral formulas Subharmonicity and its applications Convexity Hormander's solution of the $\bar\partial$ equation Solution of the Levi problem and other applications of $\bar\partial$ techniques Cousin problems, cohomology, and sheaves The zero set of a holomorphic function Some harmonic analysis Constructive methods Integral formulas for solutions to the $\bar\partial$ problem and norm estimates Holomorphic mappings and invariant metrics Manifolds Area measures Exterior algebra Vectors, covectors, and differential forms List of notation Bibliography Index.