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Field name	Details
Dewey Class	515.7
Title	Complex Convexity and Analytic Functionals ([EBook] /) / by Mats Andersson, Ragnar Sigurdsson, Mikael Passare.
Author	Andersson, Mats
Added Personal Name	Sigurdsson, Ragnar author.
Added Personal Name	Passare, Mikael author.
Other name(s)	SpringerLink (Online service)
Publication	Basel : : Birkhäuser Basel : : Imprint: Birkhäuser, , 2004.
Physical Details	XI, 164 p. : online resource.
Series	Progress in mathematics 0743-1643 ; ; 225
ISBN	9783034878715
Summary Note	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.:
Contents note	1 Convexity in Real Projective Space -- 1.1 Convexity in real affine space -- 1.2 Real projective space -- 1.3 Convexity in real projective space -- 2 Complex Convexity -- 2.1 Linearly convex sets -- 2.2 ?-convexity: Definition and examples -- 2.3 ?-convexity: Duality and invariance -- 2.4 Open ?-convex sets -- 2.5 Boundary properties of ?-convex sets -- 2.6 Spirally connected sets -- 3 Analytic Functionals and the Fantappiè Transformation -- 3.1 The basic pairing in affine space -- 3.2 The basic pairing in projective space -- 3.3 Analytic functionals in affine space -- 3.4 Analytic functionals in projective space -- 3.5 The Fantappiè transformation -- 3.6 Decomposition into partial fractions -- 3.7 Complex Kergin interpolation -- 4 Analytic Solutions to Partial Differential Equations -- 4.1 Solvability in ?-convex sets -- 4.2 Solvability and P-convexity for carriers -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-7871-5
Links to Related Works	Subject References: Convex and Discrete Geometry . Convex geometry . Discrete geometry . Functional Analysis . Functions of a Complex Variable . Functions of complex variables . Mathematics . Partial differential equations . Authors: Andersson, Mats . Passare, Mikael . Sigurdsson, Ragnar . Corporate Authors: SpringerLink (Online service) . Series: Progress in mathematics . Classification: 515.7 .

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Complex Convexity and Analytic Functionals

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