Eigenvalue asymptotics for the Schrödinger operators on the real and the complex hyperbolic spaces (Q1887203)

The authors study the spectral asymptotics of large eigenvalues of Schrödinger operators \(-\Delta + V\) on real and complex hyperbolic \(n\)-space \(H^n\) and \(H^n_c\). The non-compactness of these spaces is substituted by a growth condition on the potential \(V\) yielding compactness of the classical phase space and effective compactness of the heat kernel. A Tauberian result turns the control of the heat kernel into an estimate on the counting function which becomes semi-classical for large eigenvalues.