关于自伴算子离散谱的Harrell-Stubbe型不等式
On Harrell-Stubbe Type Inequalities for the Discrete Spectrum of a Self-Adjoint Operator
摘要：
给出了自伴算子的离散谱的一个新的证明，推广了Harrell和Stubbe的结果.一个抽象的方法-基于交换子代数，瑞利-里兹原则，和“最优”使用的柯西-施瓦茨不等式-是用来产生“无参数”，"无投影“版本的定理。我们还分析了随之而来的各种不平等的强度。结果包含经典界的特征值。扩展的各种不等式La Harrell-Stubbe的几何和物理问题。
英文摘要：
We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the Cauchy-Schwarz inequality--is used to produce ``parameter-free'', ``projection-free'' versions of their theorems. We also analyze the strength of the various inequalities that ensue. The results contain classical bounds for the eigenvalues. Extensions of a variety of inequalities à la Harrell-Stubbe are illustrated for both geometric and physical problems.
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