Abstract
One of the most important results in invariant subspace theory is the famous “Beurling’s Theorem” [1], characterizing the invariant subspaces of the shift operatorS(i.e. multiplication by the coordinate function z) on the Hardy space H 2(T).
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References
A. Beurling ,On two problems concerning linear transformations in Hilbert space, Acta. Math. 81 (1949), 239–255.
F.F. Bonsall and J. Duncan, Complete Normed Algebras, Springer Verlag, 1973.
L. de Branges,Square Summable Power Series, Springer Verlag (to appear).
H. Helson, Lectures on Invariant Subspaces.Academic Press, 1964.
K. Hoffman, Banach Spaces of Analytic Functions, Prentice Hall, 1962.
R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1990.
M. Rosenblum and J. Rovnyak, Hardy Classes and Operator Theory, Oxford University Press, 1985.
D. Singh, Brangesian Spaces in the Polydisc, Proc. Amer. Math. Soc. 110 (1990), 971–977.
D. Singh and S. Agrawal, De Branges modules in l 2 -valued Hardy spaces of the circle and the torus, Journal of Mathematical Sciences (U.N. Singh Memorial Volume) 28 (1994), 235–266.
D. Singh and S. Agrawal, De Branges spaces contained in some Banach spaces of analytic functions, Illinois Journal of Math.39 (1995), 351–357.
B.S. Yadav, D. Singh and S. Agrawal, De Branges Modules in H 2 (C k ) of the TorusinFunctional Analysis and Operator Theory, Lecture Notes in Mathematics (Number1511), Springer Verlag (1992), 55–74.
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Agrawal, S., Singh, D. (1998). De Branges Modules in H 2(C k). In: Ross, K.A., Singh, A.I., Anderson, J.M., Sunder, V.S., Litvinov, G.L., Wildberger, N.J. (eds) Harmonic Analysis and Hypergroups. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4348-5_1
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