Book Review
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Book Information:
Author:
D. Sarason
Title:
Sub-Hardy Hilbert spaces in the unit disk
Additional book information:
Lecture Notes in the Mathematical Sciences, vol. 10, Wiley,
New York,
1994,
xiv+95 pp.,
ISBN 0-471-04897-6,
$49.95$
1 D. Alpay, A. Dijksma, J. Rovnyak, and H. S. V. de Snoo, Schur functions, operator colligations, and reproducing kernel Pontryagin spaces, in preparation.
2 T. Andô, de Branges Spaces and Analytic Operator Functions, Hokkaido University, Research Institute of Applied Electricity, Division of Applied Mathematics, Sapporo, 1990.
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
Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
Louis de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), no. 1-2, 137–152. MR 772434, DOI 10.1007/BF02392821
Louis de Branges, A construction of Kreĭn spaces of analytic functions, J. Funct. Anal. 98 (1991), no. 1, 1–41. MR 1111192, DOI 10.1016/0022-1236(91)90089-N
Louis de Branges and James Rovnyak, Square summable power series, Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1966. MR 0215065
Louis de Branges and James Rovnyak, Canonical models in quantum scattering theory, Perturbation Theory and its Applications in Quantum Mechanics (Proc. Adv. Sem. Math. Res. Center, U.S. Army, Theoret. Chem. Inst., Univ. of Wisconsin, Madison, Wis., 1965) Wiley, New York, 1966, pp. 295–392. MR 0244795
Harry Dym, $J$ contractive matrix functions, reproducing kernel Hilbert spaces and interpolation, CBMS Regional Conference Series in Mathematics, vol. 71, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1989. MR 1004239, DOI 10.1090/cbms/071
James Guyker, The de Branges-Rovnyak model with finite-dimensional coefficients, Trans. Amer. Math. Soc. 347 (1995), no. 4, 1383–1389. MR 1257108, DOI 10.1090/S0002-9947-1995-1257108-3
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, Generalized interpolation in $H^{\infty }$, Trans. Amer. Math. Soc. 127 (1967), 179–203. MR 208383, DOI 10.1090/S0002-9947-1967-0208383-8
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
- 1
- D. Alpay, A. Dijksma, J. Rovnyak, and H. S. V. de Snoo, Schur functions, operator colligations, and reproducing kernel Pontryagin spaces, in preparation.
- 2
- T. Andô, de Branges Spaces and Analytic Operator Functions, Hokkaido University, Research Institute of Applied Electricity, Division of Applied Mathematics, Sapporo, 1990.
- 3
- J. A. Ball and T. L. Kriete III, Operator-valued Nevanlinna-Pick kernels and the functional models for contraction operators, Integral Equations and Operator Theory 10 (1987), 17--61, MR 88a:47013.
- 4
- A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1949), 239-255, MR 10:381.
- 5
- L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152, MR 86h:30026.
- 6
- ------, A construction of Krein spaces of analytic functions, J. Funct. Anal. 98 (1991), 1--41, MR 92k:46031.
- 7
- L. de Branges and J. Rovnyak, Square Summable Power Series, Holt, Rinehart and Winston, New York, 1966, MR 35:5909.
- 8
- ------, Canonical models in quantum scattering theory, Perturbation Theory and its Applications in Quantum Mechanics (Proc. Adv. Sem. Math. Res. Center, U.S. Army, Theoret. Chem. Inst., Univ. of Wisconsin, Madison, Wis., 1965), 1966, pp. 295--392, MR 39:6109.
- 9
- H. Dym,
Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces, and Interpolation, CBMS Regional Conference Series in Mathematics, vol 71, Amer. Math. Soc., Providence, RI, 1989, MR 90g:47003.
- 10
- J. Guyker, The de Branges-Rovnyak model with finite-dimensional coefficients, Trans. Amer. Math. Soc. 347 (1995), 1383--1389, MR 95g:46045.
- 11
- N. K. Nikol'skii and V. I. Vasyunin, Notes on two function models, The Bieberbach Conjecture (West Lafayette, Ind., 1985), Amer. Math. Soc., Providence, RI, 1986, pp. 113--141, MR 88f:47008.
- 12
- D. Sarason, Generalized interpolation in
, Trans. Amer. Math. Soc. 127 (1967), 179--203, MR 34:8193.
- 13
- ------, Shift-invariant subspaces from the Brangesian point of view, The Bieberbach Conjecture (West Lafayette, Ind., 1985), Math. Surveys Monographs, vol. 21, Amer. Math. Soc., Providence, RI, 1986, pp. (153--166), MR 88d:47014a.
Review Information:
Reviewer:
James Rovnyak
Affiliation:
University of Virginia
Email:
rovnyak@Virginia.EDU
Journal:
Bull. Amer. Math. Soc.
33 (1996), 81-85
DOI:
https://doi.org/10.1090/S0273-0979-96-00634-9
Review copyright:
© Copyright 1996
American Mathematical Society
