Eigenvalue asymptotics for the Schrödinger operators on the real and the complex hyperbolic spaces
Eigenvalue asymptotics for the Schrödinger operators on the real and the complex hyperbolic spaces
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实双曲空间和复双曲空间上薛定谔算子的特征值渐近
DOI：
10.1016/j.matpur.2004.01.005
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
S. Shirai
中科院分区：
文献类型：
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作者：
Y. Inahama;S. Shirai
研究了薛定谔算子HV=− 1 2 Δ +V在真实的和复双曲n-空间上的大特征值渐近性.这里Δ是拉普拉斯-贝尔特拉米算子，V是标量势。我们假设V是实值的，连续的，从下到上半有界的，并且在适当的意义下在无穷远处发散。然后证明了HV小于λ的特征值的个数表现为λ <$∞的半经典性质。这是一个自然推广的结果稻滨和白井[本征值渐近的薛定谔运营商的双曲平面上，J。分析：已提交出版]。
We study the large eigenvalue asymptotics for the Schrödinger operator HV=− 1 2 Δ +V on the real and the complex hyperbolic n-spaces. Here Δ is the Laplace–Beltrami operator and V is a scalar potential. We assume that V is real-valued, continuous, semi-bounded from below and diverges at infinity in an appropriate sense. Then it is proven that the number of eigenvalues of HVless than λ behaves semi-classically as λ↗∞. This is a natural generalization of the result obtained by Inahama and Shirai [Eigenvalue asymptotics for the Schrödinger operators on the hyperbolic plane, J. Funct. Anal., submitted for publication].