Beurling–Lax theorem

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 .

The result is a significant connection between operator theory with complex analysis.

See also Hardy space H2 Unilateral shift operator

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.