Beurling–Lax theorem
From HandWiki
In mathematics, the Beurling–Lax theorem is a theorem due to (Beurling 1948) and (Lax 1959) which characterizes the shift-invariant subspaces of the Hardy space [math]\displaystyle{ H^2(\mathbb{D},\mathbb{C}) }[/math]. It states that each such space is of the form
- [math]\displaystyle{ \theta H^2(\mathbb{D},\mathbb{C}), }[/math]
for some inner function [math]\displaystyle{ \theta }[/math].
See also
References
- Hazewinkel, Michiel, ed. (2001), "Beurling-Lax theorem", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=Main_Page
- Beurling, A. (1948), "On two problems concerning linear transformations in Hilbert space", Acta Math. 81: 239–255, doi:10.1007/BF02395019
- Lax, P.D. (1959), "Translation invariant spaces", Acta Math. 101 (3–4): 163–178, doi:10.1007/BF02559553
- 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.
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