The liouville equation in L1 spaces Original Research Article

We consider the first order equation View the MathML source in the Banach lattice L1(RN). By requiring a minimal amount of Sobolev regularity on the vector-field α, we show that α·▿ generates a C0-group, thereby generalizing a result of [1]. From there, we conclude the well-posedness of Liouville equation View the MathML source, for a given potential V. The comparison between the general and force-free Liouville evolution yields the existence of the wave and scattering operators, which in turn are used to prove that the spectrum of the Liouville operator is purely residual in L1(R6).