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.