Mathematical Sciences: Complex Banach Spaces

Banach空间理论是数学分析的基本工具 自1999年开始以来， 世纪。 近年来， 与数学分析的其他方面的相互作用， 调和分析和算子理论--以及概率论 理论 特别是，Banach空间方法，在手中， 具有高度创造力和强大的研究人员，已经导致了基本的 在其他领域的突破，反过来， 方法丰富了Banach空间的结构理论 自己 该领域的世界卓越中心位于 以色列、巴黎、华沙、俄亥俄州和德克萨斯州。 埃德加教授的著作反映了这种广泛的观点。 他的工作重点是使人们能够在 复杂的领域，大量的分析方法，存在于 真实的Banach空间理论。 他的工作是一个有趣的 Banach空间理论与复分析的混合，概率 （鞅）和调和分析。 在过去的工作中，他 利用伪凸域和多重次调和函数， 寻找类似物的复杂Banach空间的端点，向量 测度、鞅收敛和Choquet型定理。 埃德加教授已经打下了基础 一个可靠的理论 埃德加教授在这门课上 一个领导者，正处于起步阶段，目前的建议将携带 推进其发展。

Banach space theory is a basic tool of mathematical analysis that has been of importance since its inception at the turn of the century. In recent years, there has been a rebirth of interaction with other aspects of mathematical analysis -- such as harmonic analysis and operator theory -- and probability theory. In particular, Banach space methods, in the hands of highly creative and powerful researchers, have led to fundamental breakthroughs in these other fields, and in turn probabilistic methods have enriched the structure theory of Banach spaces themselves. World centers of excellence in this area are in Israel, Paris, Warsaw, Ohio, and Texas. Professor Edgar's work reflects this broad point of view. The thrust of his work has been to make available over the complex field, the vast array of analytic methods that exist in the theory of real Banach spaces. His work is an interesting mixture of Banach space theory with complex analysis, probability (martingales), and harmonic analysis. In past work he has utilized pseudoconvex domains and plurisubharmonic functions to find analogs for complex Banach spaces of extreme points, vector measures, martingale convergence, and Choquet-type theorems. Professor Edgar has put into place a foundation on which to build a substantial theory. This subject, in which Professor Edgar is a leader, is in its infancy, and the current proposal will carry forward its development.