On the eigenvalue asymptotics of Zonal Schrödinger operators in even metric and non-even metric

We discuss a spectral asymptotics theory of an even zonal metric and a Schrödinger operator with zonal potentials on a sphere. We decompose the eigenvalue problem into a series of one-dimensional problems. We consider the individual behavior of this series of one-dimensional problems. We find certain Weyl’s type of asymptotics on the eigenvalues