Multiparameter spectral theory and separation of variables
Multiparameter spectral theory and separation of variables
复制标题
多参数谱理论和变量分离
DOI：
10.1088/1751-8113/41/1/015209
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
B. Sleeman
中科院分区：
文献类型：
--
作者：
B. Sleeman
多参数谱理论将线性算子的经典谱理论推广到由n个谱参数连接的n个线性算子。例如，当分离变量技术被用来解决偏微分方程的边值问题时，谱参数作为分离常数出现。在本文中，我们讨论了该理论的一些基本方面，例如可解性、可交换性和抽象表示论。许多这些概念是重要的现代发展分离变量技术。这些思想在微分方程和数学物理的特殊函数中得到了应用。
Multiparameter spectral theory generalizes the classical spectral theory of linear operators to n linear operators linked by n spectral parameters. The spectral parameters arise as separation constants when, for example, separation of variables techniques are used to solve boundary-value problems for partial differential equations. In this paper, we discuss some of the fundamental aspects of the theory such as solvability, commutativity and abstract representation theory. Many of these concepts are of importance to modern developments in separation of variables techniques. The ideas are illustrated in application to differential equations and special functions of mathematical physics.