尖锥上$δ$ -相互作用的谱渐近性
Spectral asymptotics for $δ$-interactions on sharp cones
摘要：
本文研究了三维薛定谔算子与$δ$相互作用的谱。如在早期的作品中所示，这样的运营商有无穷多个本征值低于阈值的本质谱。我们专注于尖锐的圆锥，也就是说，当圆锥孔径为零的光谱特性，我们描述的本征值和本征值计数函数的渐近行为。部分结果给出的数值常数出现的解决方案的超越方程涉及修改贝塞尔函数。
英文摘要：
We investigate the spectrum of three-dimensional Schrödinger operators with $δ$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues below the threshold of the essential spectrum. We focus on spectral properties for sharp cones, that is when the cone aperture goes to zero, and we describe the asymptotic behavior of the eigenvalues and of the eigenvalue counting function. A part of the results are given in terms of numerical constants appearing as solutions of transcendental equations involving modified Bessel functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
