The asymptpotics of eigenvalues and trace formula of operator associated with one singular problem (Q361187)

The author studies the eigenvalues and eigenfunctions of the operator generated by the initial value problem \[ -y''+ x y(x) + A y(x) + q(x) y(x) = \lambda y(x) ,\, y'(0) = 0, \] where \(A\) is a self-adjoint positive definite operator in Hilbert space and \(q(x)\) is weakly measurable. The author calculates the regularized trace formula of the eigenvalues of that problem under suitable conditions.