Theory of singular perturbations with a non-smooth spectrum of the limit operator

This work is devoted to the development of the regularization method [1] for the case where the spectrum of the limit variable operator has non-smooth singularities. The case will be investigated where one of the eigenvalues of the limit operator $A(t)$ vanishes identically on certain sections of the segment [0, T], and the approach to these sections has a polynomial singularity. Such problems arise in the radio and impulse technologies.