Complex Convexity and Analytic Functionals

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.

שנה

2004

שפה

English

סדרה

Progress in Mathematics -- 225

הוצאה

Birkhäuser Basel

מהדורות

1

עמודים

164

ISBN

9783034896054

מקור הנתונים: Wikidata