𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Complex convexity and analytic functionals

✍ Scribed by Mats Andersson, Mikael Passare, Ragnar Sigurdsson

Book ID
127419347
Publisher
Birkhäuser Basel
Year
2004
Tongue
English
Weight
2 MB
Series
Progress in Mathematics
Edition
1
Category
Library
ISBN-13
9783764324209

No coin nor oath required. For personal study only.

✦ Synopsis

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.

📜 SIMILAR VOLUMES

Complex convexity and analytic functiona
Complex convexity and analytic functionals
✍ Andersson M., Passare M., Sigurdsson R. 📂 Library 📅 2004 🌐 English ⚖ 2 MB

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

Close-to-convexity, starlikeness, and co
Close-to-convexity, starlikeness, and convexity of certain analytic functions
✍ S. Owa; M. Nunokawa; H. Saitoh; H.M. Srivastava 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 339 KB

main object of the present paper is to derive several sufficient conditions for close-to-convexity, starlikeness, and convexity of certain (normalized) analytic functions. Relevant connections of some of the results obtained in this paper with those in earlier works are also provided.