Spectral theory for the q-Boson particle system

Understand

We develop spectral theory for the generator of the q-Boson (stochastic) particle system.

• Our central result is a Plancherel type isomorphism theorem for this system.
• This theorem has various implications.
• It proves the completeness of the Bethe ansatz for the q-Boson generator and consequently enables us to solve the Kolmogorov forward and backward equations for general initial data.