Mathematical Sciences: Matrices, Operators and Factorization

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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.