Book Review
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MathSciNet review:
1568033
Full text of review:
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Book Information:
Author:
Herbert Stahl and Vilmos Totik
Title:
General orthogonal polynomials
Additional book information:
Encyclopaedia of Mathematics and its Applications, vol.\ 43, Cambridge University Press, Cambridge, 1992, 250 pp., US$59.95. ISBN 0-521-41534-9.
Paul Erdös and Paul Turán, On interpolation. III. Interpolatory theory of polynomials, Ann. of Math. (2) 41 (1940), 510–553. MR 1999, DOI 10.2307/1968733
[2] W. K. Hayman and P. B. Kennedy, Subharmonic functions, vol. 1, London Math. Society Monographs (N.S.), vol. 9, Academic Press, London, 1976.
N. S. Landkof, Foundations of modern potential theory, Die Grundlehren der mathematischen Wissenschaften, Band 180, Springer-Verlag, New York-Heidelberg, 1972. Translated from the Russian by A. P. Doohovskoy. MR 0350027
Paul Nevai, Géza Freud, orthogonal polynomials and Christoffel functions. A case study, J. Approx. Theory 48 (1986), no. 1, 3–167. MR 862231, DOI 10.1016/0021-9045(86)90016-X
[5] E. A. Rahmanov, On the asymptotics of the ratio of orthogonal polynomials. II, Math. USSR-Sb. 46 (1983), 105-117.
Edward B. Saff and Vilmos Totik, Logarithmic potentials with external fields, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 316, Springer-Verlag, Berlin, 1997. Appendix B by Thomas Bloom. MR 1485778, DOI 10.1007/978-3-662-03329-6
T. J. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse Math. (6) 4 (1995), no. 1, Ji–Jiv, J1–J35 (French). Reprint of the 1894 original; With an introduction by Jean Cassinet. MR 1344720, DOI 10.5802/afst.789
[8] G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, RI, 1975.
M. Tsuji, Potential theory in modern function theory, Maruzen Co. Ltd., Tokyo, 1959. MR 0114894
J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587
- [1]
- P. Erdös and P. Turan, On interpolation. III, Ann. of Math. (2) 41 (1940), 510-553. MR 0001999 (1:333e)
- [2]
- W. K. Hayman and P. B. Kennedy, Subharmonic functions, vol. 1, London Math. Society Monographs (N.S.), vol. 9, Academic Press, London, 1976.
- [3]
- N. S. Landkof, Foundations of modern potential theory, Grundlehren Math. Wiss., vol. 190, Springer, New York, 1972. MR 0350027 (50:2520)
- [4]
- P. Nevai, Geza Freud, orthogonal polynomials and Christoffel functions, A Case Study, J. Approx. Theory 48 (1986), 3-167. MR 862231 (88b:42032)
- [5]
- E. A. Rahmanov, On the asymptotics of the ratio of orthogonal polynomials. II, Math. USSR-Sb. 46 (1983), 105-117.
- [6]
- E. B. Saff and V. Totik, Logarithmic potential with external fields (to appear). MR 1485778 (99h:31001)
- [7]
- T. J. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse (1) 8 (1894), T1-122; (1) 9 (1895), A5-47. MR 1344720 (97i:01054a)
- [8]
- G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, RI, 1975.
- [9]
- M. Tsuji, Potential theory in modern function theory, Maruzen, Tokyo, 1959. MR 0114894 (22:5712)
- [10]
- J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc. Colloq. Publ., vol. 20, Amer. Math. Soc., Providence, RI, 1969. MR 0218588 (36:1672b)
Review Information:
Reviewer:
D. S. Lubinsky
Journal:
Bull. Amer. Math. Soc.
28 (1993), 403-408
DOI:
https://doi.org/10.1090/S0273-0979-1993-00374-4
