We study infinitesimal generators of one-parameter semigroups in the unit disk \(\mathbb {D}\) having prescribed boundary regular fixed points. Using an explicit representation of such infinitesimal generators in combination with Krein–Milman Theory we obtain new sharp inequalities relating spectral values at the fixed points with other important quantities having dynamical meaning. We also give a new proof of the classical Cowen–Pommerenke inequalities for univalent self-maps of \(\mathbb {D}\).

中文翻译：

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具有指定边界固定点的半群的无穷小生成器

我们研究具有指定边界规则固定点的单位圆盘\（\ mathbb {D} \）中的一参数半群的无穷小生成器。结合Krein-Milman理论使用这种无穷小生成器的显式表示，我们获得了新的尖锐不等式，这些不等式将固定点处的频谱值与其他具有动力学意义的重要量相关联。我们还为\（\ mathbb {D} \）的单价自映射给出了经典的Cowen-Pommerenke不等式的新证明。