In mathematics, the Beurling–Lax theorem is a theorem due to and which characterizes the shift-invariant subspaces of the Hardy space . It states that each such space is of the form for some inner function . See also H2 References Jonathan R. Partington, Linear Operators and Linear Systems, An Analytical Approach to Control Theory, (2004) London Mathematical Society Student Texts 60, Cambridge University Press. Marvin Rosenblum and James Rovnyak, Hardy Classes and Operator Theory, (1985) Oxford University Press. Hardy spaces Theorems in analysis Invariant subspaces