Mathematical Sciences: Commuting Extensions of Certain Differential Operators

佩德森教授将研究交换自伴扩张 一阶偏微分算子作用于光滑 某些区域上的紧支集函数。 这种扩展可以 或者根据给定的域可以不存在。 这个项目是 部分是出于对光谱特性的理解 高阶常系数偏微分 操作员，也通过频谱之间的连接， 交换自伴扩张和域的几何。 佩德森教授还将研究这些影响， 与域相关的各种拉普拉斯算子的思想。 这个项目涉及的理论之间的联系， 微分（在许多变量）和几何在其最简单的 form. 佩德森教授将要研究的一个观点是 这些微分算子的本征值 与它们所在的n空间中的域的几何形状有关 定义了

Professor Pedersen will study commuting selfadjoint extensions of first order partial differential operators acting on smooth functions of compact support on some domain. Such extensions may or may not exist depending on the given domain. This project is motivated in part by the desire to understand spectral properties of higher order constant coefficient partial differential operators, and also by the connection between the spectrum of the commuting selfadjoint extension and the geometry of the domain. Professor Pedersen will also investigate the implications of these ideas for the various Laplace operators associated to the domain. This project involves the connection between the theory of differentiation (in many variables) and geometry in its simplest form. One of the ideas which Professor Pedersen will investigate is how the eigenvalues of these differentiation operators are related to the geometry of the domain in n-space on which they are defined.