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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
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, $49.95$

References [Enhancements On Off] (What's this?)

D. Alpay, A. Dijksma, J. Rovnyak, and H. S. V. de Snoo, Schur functions, operator colligations, and reproducing kernel Pontryagin spaces, in preparation.
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

  • Review Information:

    Reviewer: James Rovnyak
    Affiliation: University of Virginia
    Email: rovnyak@Virginia.EDU
    Journal: Bull. Amer. Math. Soc. 33 (1996), 81-85
    Review copyright: © Copyright 1996 American Mathematical Society