论文标题
经典弗里德里奇（Friedrichs）差异操作员的分类：一维标量案例
Classification of classical Friedrichs differential operators: One-dimensional scalar case
论文作者
论文摘要
ERN，Guermond和Caplain（2007）介绍的抽象弗里德里奇运营商的理论被证明是研究一阶偏微分方程的阳性对称系统的成功环境（Friedrichs，1958年），如今，众所周知的是Friedrichs Systems。最近，Antonić，Michelangeli和Erceg（2017）撰写了纯粹的操作员对弗里德里奇操作员的理论描述，允许应用通用操作员扩展理论（Grubb，1968）。在本文中，我们通过开发图形空间（最大域）的分解作为最小域和相应伴随的内核的直接总和来做出进一步的理论步骤。然后，我们研究具有可变系数的一维标量（经典）Friedrichs操作员，并对可允许的边界条件进行了完整的分类。
The theory of abstract Friedrichs operators, introduced by Ern, Guermond and Caplain (2007), proved to be a successful setting for studying positive symmetric systems of first order partial differential equations (Friedrichs, 1958), nowadays better known as Friedrichs systems. Recently, Antonić, Michelangeli and Erceg (2017) presented a purely operator-theoretic description of abstract Friedrichs operators, allowing for application of the universal operator extension theory (Grubb, 1968). In this paper we make a further theoretical step by developing a decomposition of the graph space (maximal domain) as a direct sum of the minimal domain and the kernels of corresponding adjoints. We then study one-dimensional scalar (classical) Friedrichs operators with variable coefficients and present a complete classification of admissible boundary conditions.
