The analytical theory of acoustic phonons arising in the layers of a nitride-based nanostructure, taking into account the presence of the piezoelectric effect, was developed. Proposed theory is based on the first obtained exact solutions of the system consisting of equation of motion for a semiconductor medium and Maxwell equation. The theory of the electronic spectrum renormalized by their interaction with acoustic phonons via deformation and piezoelectric potentials was developed using the method of the temperature Green's function and the Dyson equation. Direct calculations of the electron level shifts and their decay rates are performed for geometric and physical parameters of the new experimentally created nanostructure for various temperature values.