Tests for the similarity of all minimal passive realizations of a fixed transfer function (scattering or resistance matrix)

Necessary and sufficient conditions for the transfer function of a passive linear stationary scattering (or resistance) system are found ensuring that minimal systems in this class are determined by their transfer functions up to similarity. The criteria are stated in terms of a Hankel operator the symbol of which is a contractive operator-valued function defined by the transfer function and having the meaning of the inner scattering suboperator of a simple conservative scattering (respectively, resistance) system with the transfer function in question. A connection between the similarity criterion and the corona theorem and its matrix generalizations is revealed.