An improved theoretical basis is presented for the interpretation of the pulsed-neutron technique for measuring thermal-neutron absorption cross sections and transport parameters. A procedure is given for the exact solution of the Fourier-transformed, multivelocity transport equation in an infinite medium. The objective is the calculation of the decay constant of the thermalized neutron flux following an initial pulse of fast neutrons. The method used is an expansion of the decay constant and neutron spectrum in a power series in the Fourier-transform variable. The procedure is first illustrated for the case of isotropic scattering and then generalized to anistropic scattering by using the spherical harmonics expansion. The results are given in terms of integral equations whose solution involves a knowledge of the energy-transfer cross sections between thermal neutrons and the moderating material. The approach employed is to extract the maximum amount of information which is independent of these cross sections and to derive explicitly the equations involving them. It is necessary to solve these equations in order to obtain more accurate information. Finally, the relation of the infinite medium Fourier transform variable to the geometric buckling of a finite sample is discussed. It is noted that the conventional interpretation of the experiments in terms of the diffusion coefficient and diffusion cooling coefficient requires the assignment of an equivalent infinite medium buckling to each finite sample measured. The discussion in the present paper makes plausible the validity of this procedure.