无嵌入特征值的双曲三角形
Hyperbolic triangles without embedded eigenvalues
摘要：
考虑作用于双曲平面上三角形上的平方可积函数的NeumannLaplacian算子。我们表明，通用的三角形没有嵌入在其连续谱的特征值。为了证明这一结果，我们研究了退化三角形族的实解析本征值分支的行为。特别是，我们使用一个仔细的分析，这些本征值分支的模型操作符的本征值分支的交叉点附近的谱投影。
英文摘要：
We consider the Neumann Laplacian acting on square-integrable functions on a triangle in the hyperbolic plane that has one cusp. We show that the generic such triangle has no eigenvalues embedded in its continuous spectrum. To prove this result we study the behavior of the real-analytic eigenvalue branches of a degenerating family of triangles. In particular, we use a careful analysis of spectral projections near the crossings of these eigenvalue branches with the eigenvalue branches of a model operator.
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