Hilbert space structure in classical mechanics. I

@article{Deotto2003HilbertSS,
  title={Hilbert space structure in classical mechanics. I},
  author={Enrico Deotto and Ennio Gozzi and D. Mauro},
  journal={Journal of Mathematical Physics},
  year={2003},
  volume={44},
  pages={5902-5936}
}
In this paper we study the Hilbert space structure underlying the Koopman–von Neumann (KvN) operatorial formulation of classical mechanics. KvN limited themselves to study the Hilbert space of zero-forms that are the square integrable functions on phase space. They proved that in this Hilbert space the evolution is unitary for every system. In this paper we extend the KvN Hilbert space to higher forms which are basically functions of the phase space points and the differentials on phase space… Expand
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