Description

Book Synopsis
Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.

Table of Contents
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.

Function Theory of Several Complex Variables

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    A Hardback by Steven G. Krantz

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      Publisher: MP-AMM American Mathematical
      Publication Date: Publication Date: 1/30/2001 12:00:00 AM
      ISBN13: 9780821827246, 978-0821827246
      ISBN10: 0821827243

      Description

      Book Synopsis
      Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.

      Table of Contents
      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.

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