We discuss the spectral properties of singular Schrödinger operators in three dimensions with the interaction supported by an equilateral star, finite or infinite. In the finite case, the discrete spectrum is nonempty if the star arms are long enough. Our main result concerns spectral optimization: we show that the principal eigenvalue is uniquely maximized when the arms are arranged in one of the known five sharp configurations.

中文翻译：

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星形相互作用强奇异薛定谔算子的谱优化

我们讨论了奇异薛定谔算子在三个维度上的光谱特性，以及由等边星、有限或无限支持的相互作用。在有限情况下，如果星臂足够长，离散谱是非空的。我们的主要结果涉及光谱优化：我们表明，当臂以已知的五种尖锐配置之一排列时，主特征值被唯一地最大化。