Mathematical Sciences: Linear Operators and Complex Variables

9500954 Putina这个项目涉及对多变量谱理论和亚正规算子理论的持续研究。在第一个领域中，标准上同调方法将与多个复变量的硬分析技术相结合来研究函数代数上的一类Hilbert模。在第二个领域中，将在两个方向上开发和扩展求积域和次正规算子之间的一种新的对应关系。这项研究将集中在两个数学分析领域：函数论和算子论之间的几个新的、尚未完全调查的关系。预计双方都会受益，具有进一步研究以及应用于计算数学和量子物理的巨大潜力。***

9500954 Putinar This project involves continued research in multivariable spectral theory and in the theory of hyponormal operators. In the first area, standard cohomological methods will be combined with hard analysis techniques of several complex variables in the study of a class of Hilbert modules over function algebras. In the second area, a novel correspondence between quadrature domains and hyponormal operators will be exploited and expanded in both directions. The research will focus on several new and not yet fully investigated relations between two areas of mathematical analysis: function theory and operator theory. The benefits are expected to be on both sides, with a great potential of further research and with applications to computational mathematics and quantum physics. ***