We study the spectrum of the free streaming operator in the three‐dimensional case in an L 1 ‐contest. We prove that the spectrum is contained in the imaginary axis of the complex plane. We also perform a study of the semigroup generation properties of the free streaming operator and prove that the streaming operator generates a group of unitary norm in the whole space. In the half‐space case, the free streaming operator generates a group is of unitary norm only if the boundary conditions are conservative.
Acknowledgments
This work was partially supported by Par 2004—Research Project “Nuovi approcci matematici per lo studio di problemi in biologia, medicina, trasporto di fotoni e finanza” of the University of Siena funds, as well as by MURST research funds.