First, by using the 2-regularized determinant technique for Hilbert - Schmidt operators, the computation formula, infinite-product convergence, and analyticity of the 2-regularized determinant of the modified harmonic state operator infinite-dimensional linear continuous-time periodic (FDLCP) systems are derived in this paper. Second, based on these results, a 2-regularized Nyquist criterion is established for asymptotic stability analysis of a class of FDLCP systems for the first time. Third, a numeric implementation algorithm for the 2-regularized Nyquist criterion is also proposed via the staircase truncation on the harmonic transfer operator of the FDLCP system concerned. Finally, to illustrate the results of this paper, asymptotic stability of the lossy Mathieu differential equation is investigated.