Ebook: Complex Convexity and Analytic Functionals
- Tags: Functional Analysis, Functions of a Complex Variable, Partial Differential Equations, Convex and Discrete Geometry
- Series: Progress in Mathematics 225
- Year: 2004
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
A set in complex Euclidean space is called C-convex if all its intersections with complex lines are contractible, and it is said to be linearly convex if its complement is a union of complex hyperplanes. These notions are intermediates between ordinary geometric convexity and pseudoconvexity. Their importance was first manifested in the pioneering work of André Martineau from about forty years ago. Since then a large number of new related results have been obtained by many different mathematicians. The present book puts the modern theory of complex linear convexity on a solid footing, and gives a thorough and up-to-date survey of its current status. Applications include the Fantappié transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations.
Content:
Front Matter....Pages i-xi
Convexity in Real Projective Space....Pages 1-13
Complex Convexity....Pages 15-72
Analytic Functionals and the Fantappi? Transformation....Pages 73-128
Analytic Solutions to Partial Differential Equations....Pages 129-150
Back Matter....Pages 151-164
Content:
Front Matter....Pages i-xi
Convexity in Real Projective Space....Pages 1-13
Complex Convexity....Pages 15-72
Analytic Functionals and the Fantappi? Transformation....Pages 73-128
Analytic Solutions to Partial Differential Equations....Pages 129-150
Back Matter....Pages 151-164
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