Bogolubov transformations and completeness
Two complete sets of complex orthonormal basis functions in a vector space can be related to each other by linear transformations (Bogolyubov transformations) whose coefficients satisfy certain relations. It is pointed out here by some counterexamples that, conversely, these relations by themselves are not sufficient that one basis set can be expanded in terms of the other.
scientific article; zbMATH DE number 4065559