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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

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Book Information:

Author: Barry Simon
Title: Orthogonal polynomials on the unit circle, Parts 1 and 2
Additional book information: American Mathematical Society, Providence, RI, pt. 1, 2005, xxvi+466 pp., ISBN 978-0-8218-3446-6, US$89.00$; pt. 2, xxii+578 pp., ISBN 978-0-8218-3675-0, US$99.00$; ISBN 978-0-8218-3757-3, US$149.00$, set

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

  • D. Barrios Rolanía, B. de la Calle Ysern, and G. López Lagomasino, Ratio and relative asymptotics of polynomials orthogonal with respect to varying Denisov-type measures, J. Approx. Theory 139 (2006), no. 1-2, 223–256. MR 2220040, DOI 10.1016/j.jat.2005.08.006
  • K. M. Case, Orthogonal polynomials revisited, Theory and application of special functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975) Math. Res. Center, Univ. Wisconsin, Publ. No. 35, Academic Press, New York, 1975, pp. 289–304. MR 0390322
  • 3.
    M. Fekete and J. von Neumann, Über die Lage der Nullstellen gewisser Minimumpolynome, Jahresbericht der Deutschen Mathematiker-Vereinigung, 31 (1922), 128-138.
  • A. S. Fokas, A. R. It⋅s, and A. V. Kitaev, The isomonodromy approach to matrix models in $2$D quantum gravity, Comm. Math. Phys. 147 (1992), no. 2, 395–430. MR 1174420
  • 5.
    C. F. Gauss, Methodus nova integralium valores per approximationem inveniendi, Commentationes Societatis regiae scientarium Gottingensis recentiores, 3 (1814), 39-76.
  • I. M. Gel′fand and B. M. Levitan, On the determination of a differential equation by its spectral function, Doklady Akad. Nauk SSSR (N.S.) 77 (1951), 557–560 (Russian). MR 0043315
  • Leonid Golinskii, On the scientific legacy of Ya. L. Geronimus (to the hundredth anniversary), Self-similar systems (Dubna, 1998) Joint Inst. Nuclear Res., Dubna, 1999, pp. 273–281. MR 1819440
  • 8.
    L. Golinskii and V. Totik, Orthogonal Polynomials: From Jacobi to Simon, in Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday, P. Deift, F. Gesztesy, P. Perry, and W. Schlag (eds.), Proceedings of Symposia in Pure Mathematics, vol. 76, Amer. Math. Soc., Providence, RI, 2007, pp. 821-874.
  • Paul R. Halmos, I have a photographic memory, American Mathematical Society, Providence, RI, 1987. MR 934204
  • 10.
    C. G. J. Jacobi, Über Gauss' neue Methode, die Werthe der Integrale näherungsweise zu finden, Crelle J. Reine Angew. Math., 1 (1826), 301-308.
  • Michael T. Lacey, Carleson’s theorem: proof, complements, variations, Publ. Mat. 48 (2004), no. 2, 251–307. MR 2091007, DOI 10.5565/PUBLMAT_{4}8204_{0}1
  • G. G. Lorentz, Mathematics and politics in the Soviet Union from 1928 to 1953, J. Approx. Theory 116 (2002), no. 2, 169–223. MR 1911079, DOI 10.1006/jath.2002.3670
  • Attila Máté and Paul G. Nevai, Bernstein’s inequality in $L^{p}$ for $0<p<1$ and $(C,\,1)$ bounds for orthogonal polynomials, Ann. of Math. (2) 111 (1980), no. 1, 145–154. MR 558399, DOI 10.2307/1971219
  • 14.
    Math Hist, http://www-history.mcs.st-andrews.ac.uk/.
  • H. N. Mhaskar, Introduction to the theory of weighted polynomial approximation, Series in Approximations and Decompositions, vol. 7, World Scientific Publishing Co., Inc., River Edge, NJ, 1996. MR 1469222
  • Paul Nevai, Letter to a friend, J. Approx. Theory 46 (1986), no. 1, 3–8. Papers dedicated to the memory of Géza Freud. MR 835719, DOI 10.1016/0021-9045(86)90078-X
  • 17.
    Math Intelligence Test, http://www.math.ohio-state.edu/~nevai/QUIZ/quiz.txt.
    18.
    A. B. J. Novikoff, Special System of Orthogonal Polynomials, Ph.D. Dissertation, Stanford University, 1954.
    19.
    I. V. Ostrovskii, Kharkov Mathematical Society, in ``European Mathematical Society'', Newsletter No. 34, December, 1999, pp. 26-27, and http://emis.kaist.ac.kr/newsletter/newsletter34. pdf.
  • George Pólya, The Pólya picture album: encounters of a mathematician, Birkhäuser Boston, Inc., Boston, MA, 1987. Edited and with an introduction and a biography by G. L. Alexanderson. MR 898436
  • Barry Simon, Orthogonal polynomials on the unit circle. Part 1, American Mathematical Society Colloquium Publications, vol. 54, American Mathematical Society, Providence, RI, 2005. Classical theory. MR 2105088, DOI 10.1090/coll054.1
  • Barry Simon, Orthogonal polynomials on the unit circle. Part 1, American Mathematical Society Colloquium Publications, vol. 54, American Mathematical Society, Providence, RI, 2005. Classical theory. MR 2105088, DOI 10.1090/coll054.1
  • 23.
    B. Simon, Orthogonal Polynomials on the Unit Circle, the website, http://www.math.caltech.edu/opuc.html.
  • Barry Simon, OPUC on one foot, Bull. Amer. Math. Soc. (N.S.) 42 (2005), no. 4, 431–460. MR 2163705, DOI 10.1090/S0273-0979-05-01075-X
  • 25.
    B. Simon, CMV matrices: Five years after, in Proceedings of the W. D. Evans' 65th Birthday Conference, J. Comput. Appl. Math., XXX (2007), to appear, and http://arxiv.org/abs/math.SP/0603093.
  • Gábor Szegő, Orthogonal polynomials, 4th ed., American Mathematical Society Colloquium Publications, Vol. XXIII, American Mathematical Society, Providence, R.I., 1975. MR 0372517
  • Gábor Szegő, Collected papers. Vol. 1, Contemporary Mathematicians, Birkhäuser, Boston, Mass., 1982. 1915–1927; Edited by Richard Askey; Including commentaries and reviews by George Pólya, P. C. Rosenbloom, Askey, L. E. Payne, T. Kailath and Barry M. McCoy. MR 674482
  • Vilmos Totik, Weighted approximation with varying weight, Lecture Notes in Mathematics, vol. 1569, Springer-Verlag, Berlin, 1994. MR 1290789, DOI 10.1007/BFb0076133
  • Vilmos Totik, Asymptotics for Christoffel functions for general measures on the real line, J. Anal. Math. 81 (2000), 283–303. MR 1785285, DOI 10.1007/BF02788993
  • Vilmos Totik, Orthogonal polynomials, Surv. Approx. Theory 1 (2005), 70–125. MR 2221567
  • David S. Watkins, Some perspectives on the eigenvalue problem, SIAM Rev. 35 (1993), no. 3, 430–471. MR 1234638, DOI 10.1137/1035090

  • Review Information:

    Reviewer: Paul Nevai
    Affiliation: The Ohio State University
    Email: paul@nevai.us
    Journal: Bull. Amer. Math. Soc. 44 (2007), 447-470
    Published electronically: April 10, 2007
    Review copyright: © Copyright 2007 American Mathematical Society