Oscillation theory locates the spectrum of a differential equation by counting the zeros of its solutions. We present a version of this theory for canonical systems $Ju'=-zHu$ and then use it to discuss semibounded operators from this point of view. Our main new result is a characterization of systems with purely discrete spectrum in terms of the asymptotics of their coefficient functions; we also discuss the exponential types of the transfer matrices.

中文翻译：

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振荡理论和半有界典范系统

振荡理论通过计算其解的零点来定位微分方程的频谱。我们为规范系统$ Ju'=-zHu $提供了该理论的一个版本，然后从这个角度使用它来讨论半界算子。我们的主要新结果是根据系数函数的渐近性来表征具有纯离散光谱的系统。我们还讨论了转移矩阵的指数类型。