Beurling–Lax theorem

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In mathematics, the Beurling–Lax theorem is a theorem due to Beurling (1949) and Lax (1959) which characterizes the shift-invariant subspaces of the Hardy space $H^2(\mathbb{D},\mathbb{C})$ . It states that each such space is of the form

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

for some inner function $θ$ .

[edit] References

Ball, J. A. (2001), “Beurling–Lax theorem”, in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104
Beurling, A. (1949), “On two problems concerning linear transformations in Hilbert space”, Acta Math. 81: 239–255, MR 0027954, DOI 10.1007/BF02395019
Lax, P.D. (1959), “Translation invariant spaces”, Acta Math. 101: 163–178, MR 0105620 , DOI 10.1007/BF02559553

Categories: Hardy spaces

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