  In this paper we present a generic formulation of the linearized dynamical
equations governing small adiabatic radial oscillations of relativistic stars.
The dynamical equations are derived by taking into consideration those effects
of viscosity and thermal conductivity of neutron-star matter which directly
determine the minimum period of observable pulsars. A variational principle is
applied to determine a discrete set of eigenfunctions with complex eigenvalues.
The real and imaginary parts of eigenvalues represent the squared natural
frequencies and relaxation time of radial oscillations of non-rotating neutron
stars, respectively. We provide a suitable framework which may be supplemented
with various potential species of cold-nuclear-matter models to compute the
spectra of the normalized eigenfrequencies with a certain numerical precision.
In the last section, we provide a qualitative estimation of the rate at which
viscosity and thermal conductivity drain the kinetic energy of radial
oscillation mode in reasonably uniform neutron stars, without relying on
explicit numerical computations.
