Mathematical Sciences: Linear Operators and Complex Variables

小行星9500954 该项目涉及多变量谱理论和亚正规化理论的继续研究 运营商在第一个领域，标准的上同调方法将与几个复杂的硬分析技术相结合， 一类函数上Hilbert模研究中的变量 代数在第二个领域， 正交域和亚正规算子将被利用， 向两个方向扩展。 该研究将集中在几个新的和尚未完全 研究了两个数学分析领域之间的关系： 函数论和算子论。预计这些好处将 双方，具有进一步研究的巨大潜力， 应用于计算数学和量子力学 物理学 ***

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. ***