Mathematical Sciences: Subnormal Operators and Related Topics

算子理论是现代分析中的一个中心学科。 它的起源在于研究数学物理和部分 微分方程在世纪早期。 因此 我们发现，在量子力学理论中， 平衡，振动，量子理论等可以研究 有效地通过模拟现象的积分方程。 因此，从希尔伯特丰富的思想中， 诺依曼和其他巨人认为算子理论的主题 在这样的调查中成长为中心地位，在核心 数学也是。 这种方法的核心是 对算子谱的深入研究， 不变子空间的伴随研究。 为了所谓的 自伴算子，这个理论现在是一个标准的技术 在整个分析中，谱定理提供了 为所有这些运营商提供必要的构建模块。 尽管未 同样完整的是，谱理论 理解为自伴的广泛推广 情况;即，“正常”的运营商。 目前的前沿， 因此，在对这种结构理论的研究中， 非常态理论 康威教授长期以来一直是研究 次正规算子，一个广泛的一类算子，出现在 应用程序，并且有足够的残差正常 试图更深入地了解其固有的信息 结构 最近的结果，例如低于正常的事实， 算子是自反的，具有不变子空间，给出了 这对研究它们的光谱特性是一个额外的推动力。 由于在复变函数中出现的许多显式算子 理论、微分几何和逼近理论是 低于正常，有一个广泛的发展中的相互作用。 康威教授将研究次正规算子， 自然地在哈代空间的行动，从而探索 与功能理论的互动 他还将调查 次正规算子的内部结构理论 考虑酉等价，束转移， 与一般算子理论的关系

Operator theory is a central discipline in Modern Analysis. Its origins lie in the study of mathematical physics and partial differential equations in the early twentieth century. Thus, it was seen that numerous physical problems in the theory of equilibria, vibration, quantum theory, etc. could be studied productively via the integral equations that model the phenomena. So it has been, that from the fertile minds of Hilbert, von Neumann, and other giants that the subject of operator theory has grown to a central position in such investigations, and in core mathematics as well. At the heart of this methodology is the deep investigation of the spectrum of an operator and the concommitant study of its invariant subspaces. For the so-called self-adjoint operators, this theory is now a standard technique throughout analysis, and the spectral theorem provides the necessary building blocks for all such operators. Although not quite as complete, spectral theory is significantly well understood for an extensive generalization of the self-adjoint case; viz., the "normal" operators. The current frontier, therefore, in the study of this structure theory rests in the non-normal theory. Professors Conway has long been a leader in the study of subnormal operators, a broad class of operators that arise in applications, and for which there is enough residual normal information to attempt a deeper understanding of their inherent structure. Recent results, suchas the fact that subnormal operators are reflexive and have invariant subspaces, have given an added impetus to the study of their spectral properties. Since many explicit operators that arise in complex function theory, differential geometry, and approximation theory are subnormal, there is a broad range of developing interaction. Professor Conway will study subnormal operators that arise naturally in actions on Hardy spaces, thereby exploring the interaction with function theory. He will also investigate the internal structure theory of subnormal operators, with particular consideration of unitary equivalence, bundle shifts, and the relationship with general operator theory.