# Beurling–Lax theorem

In mathematics, the Beurling–Lax theorem is a theorem due to Template:Harvtxt and Template:Harvtxt which characterizes the shift-invariant subspaces of the Hardy space ${\displaystyle H^{2}({\mathbb {D} },{\mathbb {C} })}$. It states that each such space is of the form

${\displaystyle \theta H^{2}({\mathbb {D} },{\mathbb {C} }),}$

## References

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• 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.