Mathematical Sciences: Multivariable Spectral Theory and Complex Analysis

普蒂纳将调查两组问题。第一个是关于多元Bergman空间上的Toeplitz算子及其与多复变函数论的关系。他将把这类算子的谱问题与边界具有L2增长控制的伪凸域中的函数理论联系起来。第二组问题与欧几里得n-空间中的矩理论有关。Putina将尝试通过使用特定的算子理论来确定解决半代数子集上的某些矩问题的方法。算子论是研究矩阵的无限维广义的数学部分。特别地，当被限制在有限维子空间时，算子具有通常的线性性质，因此可以用矩阵来表示。算子理论中的中心问题是根据伴随算子(例如伴随算子)或基础空间对满足附加条件的算子进行分类。算符理论是许多数学的基础，也是数学在其他科学中的许多应用。

Putinar will investigate two sets of problems. The first concerns Toeplitz operators on multivariable Bergman spaces and their relevance for the function theory of several complex variables. He will relate the spectral problems for this class of operators to the theory of functions in pseudoconvex domains with L2-growth control at the boundary. The second set of problems is related to the theory of moments in Euclidean n- space. Putinar will try to determine methods for solving certain moment problems on semialgebraic subsets by using specific operator theories. Operator theory is that part of mathematics that studies the infinite dimensional generalizations of matrices. In particular, when restricted to finite dimensional subspaces, an operator has the usual linear properties, and thus can be represented by a matrix. The central problem in operator theory is to classify operators satisfying additional conditions given in terms of associated operators (e.g. the adjoint) or in terms of the underlying space. Operator theory underlies much of mathematics, and many of the applications of mathematics to other sciences.