The de Branges-Rovnyak model

Guyker, James

doi:10.1090/S0002-9939-1991-1031663-2

The de Branges-Rovnyak model
HTML articles powered by AMS MathViewer

by James Guyker

Proc. Amer. Math. Soc. 111 (1991), 95-99

DOI: https://doi.org/10.1090/S0002-9939-1991-1031663-2

PDF | Request permission

Abstract:

A characterization, extending results of A. Beurling, L. de Branges and J. Rovnyak, of those Hilbert spaces of formal power series, which are isometrically equal to a de Branges-Rovnyak (scalar-valued) function space $\mathcal {H}(b)$, is obtained.

References

Joseph A. Ball and Thomas L. Kriete III, Operator-valued Nevanlinna-Pick kernels and the functional models for contraction operators, Integral Equations Operator Theory 10 (1987), no. 1, 17–61. MR 868573, DOI 10.1007/BF01199793
Arne Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 239–255. MR 27954, DOI 10.1007/BF02395019

Square summable power series

Louis de Branges and James Rovnyak, Square summable power series, Holt, Rinehart and Winston, New York-Toronto-London, 1966. MR 0215065

A characterization of a class of Hilbert spaces of power series

N. K. Nikol′skiĭ and V. I. Vasyunin, Notes on two function models, The Bieberbach conjecture (West Lafayette, Ind., 1985) Math. Surveys Monogr., vol. 21, Amer. Math. Soc., Providence, RI, 1986, pp. 113–141. MR 875237, DOI 10.1090/surv/021/11
Donald Sarason, Shift-invariant spaces from the Brangesian point of view, The Bieberbach conjecture (West Lafayette, Ind., 1985) Math. Surveys Monogr., vol. 21, Amer. Math. Soc., Providence, RI, 1986, pp. 153–166. MR 875239, DOI 10.1090/surv/021/13
Donald Sarason, Shift-invariant spaces from the Brangesian point of view, The Bieberbach conjecture (West Lafayette, Ind., 1985) Math. Surveys Monogr., vol. 21, Amer. Math. Soc., Providence, RI, 1986, pp. 153–166. MR 875239, DOI 10.1090/surv/021/13