Mathematical Sciences: Matrices, Operators and Factorization

Spitkovsky教授将对某些主题进行研究 在运营商和矩阵理论，他一直参与了 过去几年。 他将调查以下问题 （1）非光滑扇形矩阵的因式分解 轮廓，（2）因子分解乘数的局部行为，（3） 左和右部分索引之间的连接，（4） 分段拟连续矩阵的可分解性（5） 概周期矩阵的因子分解与正扩张 （6）谱的推广 配置定理;（7）幂不等式的推广 数字范围。 矩阵值函数的因子分解（分解为其他矩阵 具有特定属性）是许多领域的重要工具， 数学及其应用，如系统理论， 概率论，微分和积分方程。 Spitkovsky教授的研究是这些领域的基础。

Professor Spitkovsky will conduct research on certain topics in operator and matrix theory in which he has been involved for the past several years. He will investigate problems in the following areas: (1) factorization of sectorial matrices on non-smooth contours, (2) local behavior of factorization multipliers, (3) connections between left and right partial indices, (4) factorizability of piecewise-quasi-continuous matrices, (5) factorization of almost periodic matrices and positive extensions of almost-periodic functions, (6) generalizations of the spectrum assignment theorem, and (7) generalizations of the power inequality for numerical range. Factorization of matrix valued functions (into other matrices with specific properties) is an important tool in many areas of mathematics and its applications such as systems theory, probability theory, and differential and integral equations. Professor Spitkovsky's research is basic to these areas.