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This book is dedicated to the memory of Mikael Passare, an outstanding Swedish mathematician who devoted his life to developing the theory of analytic functions in several complex variables and exploring geometric ideas first-hand. It includes several papers describing Mikael's life as well as his contributions to mathematics, written by friends of Mikael's who share his attitude and passion for science. A major section of the book presents original research articles that further develop Mikael's ideas and which were written by his former students and co-authors. All these mathematicians...

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 Andre 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...

This 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 Fantappie transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations.