Generalized factorization for a class 2×2 matrix functions with rationally-independent entries

Necessary and sufficient conditions for the existence of canonical generalized factorizations are given for a class of non-rational 2×2 matrix-valued functions. Explicit formulas for the factors are derived. The class considered is related to a class studied by Rawlins and Williams from the point of view of function-theoretic factorization. The method of analysis followed in the paper involves solving a certain non-linear singular integral equation. An example is included.