Asymptotic representation of projector kernel for 2D harmonic oscillator in a strip

The study of the asymptotic behavior of the eigenprojector kernel is a key point in obtaining formulas for the regularized traces of bounded perturbations for discrete two-dimensional model differential operators of mathematical physics. In this paper, we consider a 2D harmonic oscillator in a strip. The stationary phase method is used to study the asymptotics of the projector kernel.