US-India Cooperative Research: Extremal Structures in Banach Spaces

描述：该奖项支持美印合作研究：巴拿赫空间的极端结构。爱荷华大学的林教授和三位印度数学家，印度统计研究所的P. Bandyopadhyay和T.S.S.R.K. Rao以及本地治里大学的V. Indumathi将研究巴拿赫空间的几何。在早期的工作中，他们完全解决了巴拿赫空间中嵌套球序列的同构性质。他们建议将这个解决方案扩展到等距性质。此外，他们将研究各种球分离性质的推广和度量投影到近端子空间的连续性。研究范围：巴拿赫空间几何是泛函分析中一个非常活跃的研究分支，在纯数学和应用数学中有着广泛的应用。凸分析是许多数学分支的主要工具，包括概率论、小波理论、偏微分方程和计算理论，主要应用于数学、金融、经济学、管理科学和基础科学。美国PI是一个成熟的研究机构，而印度PI拥有很高的声誉。这是一次有价值的合作，将促进与印度优秀机构的互动，并将为研究生、初级同事和少数民族提供机会。印度政府科学技术部（DST）在国家科学基金会/DST联合项目下资助了这项研究。

0352523Lin Description: This award supports the US-India Cooperative Research: Extremal Structures in Banach Spaces. Professor Bor-Luh Lin, University of Iowa and three Indian mathematicians, P. Bandyopadhyay and T.S.S.R.K. Rao, Indian Statistical Institute and V. Indumathi, University of Pondicherry will study the geometry of Banach spaces. In earlier work, they solved completely the isomorphic properties of nested sequences of balls in Banach spaces. They propose to extend this solution to the isometric properties. Additionally, they will study generalizations of various ball separation properties and the continuity of metric projections onto proximinal subspaces. Scope: Geometry of Banach spaces is currently a very active branch of research in Functional Analysis with wide-ranging applications in pure and applied mathematics. Convex analysis is a major tool in many branches of mathematics including probability theory, wavelet theory, partical differential equations and computing theory with major applications to mathematical finances, economics, management sciences, and to basic sciences. The US PI is an established researcher and the Indian group has a strong reputation. It is a valuable collaboration that will promote interactions with excellent Indian instituions and will provide opportunities for graduate students, junior colleagues, and minorities. The Government of India's Department of Science and Technology (DST) funds this research under the NSF/DST joint program.