Tao Qian “Blaschke Decomposition of Matrix-valued functions”

We show that on the n-torus with the matrix valued Hardy space case one can perform a similar Blaschke product decomposition like in the classical case. In the latter case this type decomposition is an implementation of the direct sum decomposition of the Hardy space into zero-based invariant subspaces and the corresponding backward shift invariant subspaces involving the Beurling Theorem.