A new Koopman-von Neumann framework uses reproducing kernel Hilbert spaces and symmetric Fock space dilations to represent non-unitary classical evolution unitarily, without choosing a volume measure on the state space.
Anisotropic H¨ older and Sobolev Spaces for Hyperbolic Diffeomorphisms
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Measure-free Koopman-von Neumann Dynamics and Noncommutative Geometry
A new Koopman-von Neumann framework uses reproducing kernel Hilbert spaces and symmetric Fock space dilations to represent non-unitary classical evolution unitarily, without choosing a volume measure on the state space.