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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
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
- 1.
- D. Barrios, B. de la Calle, and G. López Lagomasino, Ratio and relative asymptotics of polynomials orthogonal with respect to varying Denisov type measures, J. Approx. Theory, 139 (2006) (volume dedicated to Barry Simon), 223-256. MR 2220040 (2006m:42002)
- 2.
- K. M. Case, Orthogonal polynomials revisited, in ``Theory and Application of Special Functions'', R. A. Askey (Editor), Proceedings of an advanced seminar sponsored by the Mathematics Research Center, University of Wisconsin-Madison, March 21-April 2, 1975. Academic Press, New York, 1975, pp. 289-304. MR 0390322 (52:11148)
- 3.
- M. Fekete and J. von Neumann, Über die Lage der Nullstellen gewisser Minimumpolynome, Jahresbericht der Deutschen Mathematiker-Vereinigung, 31 (1922), 128-138.
- 4.
- A. S. Fokas, A. R. Its, and A. V. Kitaev, The isomonodromy approach to matrix models in 2D quantum gravity, Comm. Math. Phys., 147 (1992), 395-430. MR 1174420 (93h:81115)
- 5.
- C. F. Gauss, Methodus nova integralium valores per approximationem inveniendi, Commentationes Societatis regiae scientarium Gottingensis recentiores, 3 (1814), 39-76.
- 6.
- I. M. Gel'fand and B. M. Levitan, On the determination of a differential equation by its spectral function. (Russian), Doklady Akad. Nauk SSSR (N.S.), 77 (1951), 557-560. MR 0043315 (13:240f)
- 7.
- L. Golinskii, On the scientific legacy of Ya. L. Geronimus (to the hundredth anniversary), in ``Self-Similar Systems'', V. B. Priezzhev and V. P. Spiridonov (Editors), Proceedings of the International Workshop held in Dubna, July 30-August 7, 1998, Joint Inst. Nuclear Res., Dubna, 1999, pp. 273-281, and http://theor.jinr.ru/meetings/98/sss/proceedings.html. 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.
- 9.
- P. Halmos, I Have a Photographic Memory, American Mathematical Society, Providence, RI, 1987. MR 934204 (89f:01067)
- 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.
- 11.
- M. T. Lacey, Carleson's theorem: proof, complements, variations, Publ. Mat., 48 (2004), no. 2, 251-307, and http://www.arxiv.org/abs/math.CA/0307008. MR 2091007 (2005e:42020)
- 12.
- G. G. Lorentz, Mathematics and politics in the Soviet Union from 1928 to 1953, J. Approx. Theory, 116 (2002), 169-223, and http://www.math.ohio-state.edu/AT/LORENTZ/JAT02-0001_final.pdf. MR 1911079 (2003c:01059)
- 13.
- A. Máté and P. Nevai, Bernstein's inequality in for and bounds for orthogonal polynomials, Ann. Math., 111 (1980), 145-154. MR 558399 (81c:42003)
- 14.
- Math Hist, http://www-history.mcs.st-andrews.ac.uk/.
- 15.
- H. N. Mhaskar, Introduction to the theory of weighted polynomial approximation, Series in Approximations and Decompositions, Vol. 7, World Scientific, 1996. MR 1469222 (98i:41014)
- 16.
- P. Nevai, Letter to a friend, J. Approx. Theory, 46 (1986), 4-8. MR 835719 (87j:01062a)
- 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.
- 20.
- G. Pólya, The Pólya Picture Album: Encounters of a Mathematician, G. L. Alexanderson (Editor), Birkhäuser, 1987. MR 898436 (88i:01125)
- 21.
- B. Simon, Orthogonal Polynomials on the Unit Circle, V.1: Classical Theory, AMS Colloquium Series, American Mathematical Society, Providence, RI, 2005. MR 2105088 (2006a:42002a)
- 22.
- B. Simon, Orthogonal Polynomials on the Unit Circle, V.2: Spectral Theory, AMS Colloquium Series, American Mathematical Society, Providence, RI, 2005. MR 2105089 (2006a:42002b)
- 23.
- B. Simon, Orthogonal Polynomials on the Unit Circle, the website, http://www.math.caltech.edu/opuc.html.
- 24.
- B. Simon, OPUC on one foot, Bull. Amer. Math. Soc. (N.S.), 42 (2005), no. 4, 431-460, and http://www.ams.org/bull/2005-42-04/S0273-0979-05-01075-X/S0273-0979-05-01075-X. pdf. MR 2163705 (2006e:42039)
- 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.
- 26.
- G. Szego, Orthogonal Polynomials, AMS Colloquium Series, Vol. 23, American Mathematical Society, Providence, R.I., 1939; 4th edition, 1975. MR 0372517 (51:8724)
- 27.
- G. Szego, Collected papers, Vol. 1, 1915-1927, edited by R. Askey, Birkhäuser, 1982. MR 674482 (84d:01082a)
- 28.
- V. Totik, Weighted approximation with varying weight, Springer Lecture Notes, Vol. 1569, Springer-Verlag, Berlin, 1994. MR 1290789 (96f:41002)
- 29.
- V. Totik, Asymptotics for Christoffel functions for general measures on the real line, J. Anal. Math., 81 (2000), 283-303. MR 1785285 (2001j:42021)
- 30.
- V. Totik, Orthogonal Polynomials, Surveys in Approximation Theory, online journal at http://www.math.technion.ac.il/, 1 (2005), 70-125, and http://www.math.technion.ac.il/sat/papers/3/. MR 2221567 (2007a:42055)
- 31.
- David S. Watkins, Some perspectives on the eigenvalue problem, SIAM Review, 35 (1993), 430-471. MR 1234638 (94h:65039)
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