International cooperative research on homogeneous operators

这个奖项是由OISE和DMS共同资助的，并将部分支持纽约州立大学H H雷曼学院的A.Koranyi教授和印度科学研究所的G.Misra教授之间的合作研究。研究将集中在齐次算子上。这在Hilbert空间上形成了一类重要的算子。G·米斯拉教授是这方面的主要专家。Cowen-Douglas类中所有齐次算子的分类和显式刻画是该领域中的一个重要的公开问题。在过去的三年里，A.Koranyi和G.Misra一直在联合研究这个问题。由此产生了两个文献，在一个重要的特例中给出了完整的分类，并证明了各种性质。这项研究的继续有望导致在一般情况下的完整分类和有关问题的结果，特别是关于扩张理论的结果。在此之后，将尝试将至少部分结果推广到与有界对称域相关的交换算子的n元组的情况。该建议的智力优点在于通过结合不同数学分支的思想来解决算子理论中一些长期悬而未决的问题。这将是算子理论的实质性进步。更广泛的影响包括推进算子理论和广泛传播结果，以期对所有在该领域工作的人有用。这将提供一种可能在物理学中应用的方法，并将对城市大学研究生院和班加罗尔印度科学研究所的教学和研究活动产生有益的影响。该项目的规模足够大，学生和初级研究人员可以参与其中。

KoranyiThis award is being co-funded OISE and DMS and will partially support collaborative research between Professor A. Koranyi of CUNY, H H Lehman College, and Professor G. Misra if Indian Institute of Science. The research will focus on homogeneous operators. These form an important class of operators on Hilbert space. Professor G. Misra is the leading expert on them. There are important open questions in the field, such as the classification and explicit description of all homogeneous operators in the Cowen-Douglas class. A. Koranyi and G. Misra have been doing joint research on this problem for the last three years. Two publications have resulted from this, giving a full classification in an important special case and proving various properties. The continuation of this research is expected to lead to a complete classification in the general case and to results about related problems, in particular about dilation theory. After this, it will be attempted to extend at least some of the results to the case of n-tuples of commuting operators associated to bounded symmetric domains.The intellectual merit of the proposal consists in solving some long open problems of operator theory by the combination of ideas from different branches of mathematics. This will constitute substantial progress in operator theory. The broader impacts include advancing operator theory and widely distributing the results in a wy to be useful to all working in the field. This will furnish a method that may have applications in physics and will have a beneficial effect on teaching and research activities both at the CUNY Graduate Center and at the Indian Institute of Science in Bangalore. The project is large enough for students and junior researchers to participate in it.