论文标题
普遍的Birman-Schwinger原则
The Generalized Birman-Schwinger Principle
论文作者
论文摘要
我们在非自我支持的环境中证明了普遍的Birman-Schwinger原则。特别是，我们对感兴趣的基本操作员（例如Schrödinger经营者）和相关的Birman-Schwinger操作员的几何和代数多重性提供了详细的讨论，并提供了对两家运营商的一般特征向量相关的Jordan链的仔细研究。在分析过程中，我们还研究了强有力分析的操作员值函数的代数和几何多重性以及广义特征向量的相关Jordan链。我们还将代数多重性与分析运算符值函数索引的概念联系起来，并为一对非自动加速操作员提供了一般的Weinstein-Aronszajn公式。
We prove a generalized Birman-Schwinger principle in the non-self-adjoint context. In particular, we provide a detailed discussion of geometric and algebraic multiplicities of eigenvalues of the basic operator of interest (e.g., a Schrödinger operator) and the associated Birman-Schwinger operator, and additionally offer a careful study of the associated Jordan chains of generalized eigenvectors of both operators. In the course of our analysis we also study algebraic and geometric multiplicities of zeros of strongly analytic operator-valued functions and the associated Jordan chains of generalized eigenvectors. We also relate algebraic multiplicities to the notion of the index of analytic operator-valued functions and derive a general Weinstein-Aronszajn formula for a pair of non-self-adjoint operators.
