Based on the analytic perturbation theory of linear operators using the method of constructing holomorphic functions for transforming the vibrational-rotational Hamiltonian. Built operator function is used to investigate the excited vibrational states and transitions between them. Formulas are obtained for the matrix elements and the absolute intensities of the spectral lines as a function of rotational and vibrational quantum numbers for the main bands of infrared absorption spectra of polyatomic molecules.