Beurling–Lax theorem

Beurling–Lax theorem 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 {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} ),} for some inner function {displaystyle theta } .

See also H2 References Ball, J. A. (2001) [1994], "Beurling-Lax theorem", Encyclopedia of Mathematics, EMS Press Beurling, A. (1949), "On two problems concerning linear transformations in Hilbert space", Acta Math., 81: 239–255, doi:10.1007/BF02395019, MR 0027954 Lax, P.D. (1959), "Translation invariant spaces", Acta Math., 101 (3–4): 163–178, doi:10.1007/BF02559553, MR 0105620 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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