The Boltzmann equation is linearized around total equilibrium and solved by means of a projection operator, which projects the single particle distribution function on the slowly varying local density, temperature, and stream velocity. For small spatial variations the exact solution approaches asymptotically to the Chapman-Enskog normal solution with a relaxation time of the order of the mean free time. The heat current and pressure tensor obtained from this solution are connected with the gradients of the local temperature and stream velocity in a nonlocal and noninstantaneous manner by means of time correlation kernels. For large times and small gradients, the transport currents are expanded in gradients of the local densities, yielding expressions for the Navier-Stokes and linear Burnett coefficients as matrix elements of the linearized Boltzmann collision operator. An Onsager relation between two linear Burnett coefficients is demonstrated.