Complex Convexity and Analytic Functionals
Π΄Π΅Ρ 2012. Β· Progress in Mathematics 225. ΠΊΡΠΈΠ³Π° Β· BirkhΓ€user
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O ovoj e-knjizi
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 AndrΓ© 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 FantappiΓ© transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations.
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