The support of the equilibrium measure in the presence of a monomial external field on [-1, 1]

Transactions of the American Mathematical Society

Volumn 351, Issue 11, 1999, Pages 4561-4584

  Damelin, S B ^a   Kuijlaars, A B J ^b  

^a UNIVERSITY OF THE WITWATERSRAND   (South Africa)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Balayage; Equilibrium measure; External field; Potential theory; Weighted polynomials

Indexed keywords

EID: 22844454647     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-99-02509-x     Document Type: Article

References (21)

1. P. Borwein and T. Erdélyi, Polynomials and Polynomial Inequalities, Springer-Verlag, New York, 1995. MR 97e:41001
2. p (0 < p ≤ ∞), J. Approx. Theory 94 (1998), 333-382. CMP 98:17
3. P. Deift, T. Kriecherbauer and K. T-R McLaughlin, New results on the equilibrium measure for logarithmic potentials in the presence of an external field, 3. Approx. Theory 95 (1998), 388-475. CMP 99:05
4. P. Deift and K. T-R McLaughlin, A continuum limit of the Toda lattice, Mem. Amer. Math. Soc. 624 (1998). MR 98h:58076
5. p (0 < p ≤ ∞), Constr. Approx. 13 (1997), 99-152. MR 97k:41028
6. F.D. Gakhov, Boundary Value Problems, Pergamon Press, Oxford, 1966. MR 33:6311
7. A. A. Gonchar and E. A. Rakhmanov, Equilibrium measure and the distribution of zeros of extremal polynomials, Mat. Sb. 125 (1984), 117-127. English transi: Math. USSR-Sb. 53 (1986), 119-130. MR 86f:41002
8. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, Orlando, 1980. MR 81g:33001
9. K. G. Ivanov and V. Totik, Fast decreasing polynomials, Constr. Approx. 6 (1990), 1-20. MR 90k:26023
10. S. Karlin and W. J. Studden, Tchebycheff Systems with Applications in Analysis and Statistics, Wiley, New York, 1966. MR 34:4757
11. A. B. J. Kuijlaars and P. D. Dragnev, Equilibrium problems associated with fast decreasing polynomials, Proc. Amer. Math. Soc. 127 (1999), 1065-1074. CMP 99:06
12. A. B. J. Kuijlaars and W. Van Assche, A problem of Totik on fast decreasing polynomials, Constr. Approx. 14 (1998), 97-112. MR 99b:26026
13. G. G. Lorentz, M. von Golitschek and Y. Makovoz, Constructive Approximation, Advanced Problems, Springer-Verlag, Berlin, 1996. MR 97k:41002
14. D. S. Lubinsky and E. B. Saff, Strong Asymptotics for Extremal Polynomials associated with Weights on ℝ, Lcct. Notes in Math. vol. 1305, Springer-Verlag, Berlin, 1988. MR 89m:41013
15. H. N. Mhaskar, Introduction to the Theory of Weighted Polynomial Approximation, World Scientific, Singapore, 1996. MR 98i:41014
16. H. N. Mhaskar and E. B. Saff, Where does the sup norm of a weighted polynomial live?, Constr. Approx. 1 (1985), 71-91. MR 86a:41004
17. E. A. Rakhmanov, On asymptotic properties of polynomials orthogonal on the real axis, Mat. Sb. 119 (1982), 163-203. English transi.: Math. USSR-Sb. 47 (1984), 155-193. MR 84e:42025
18. E. B. Saff and V. Totik, Logarithmic Potentials with External Fields, Springer-Verlag, New York, 1997. CMP 98:05
19. H. Stahl and V. Totik, General Orthogonal Polynomials, Cambridge University Press, Cambridge, 1992. MR 93d:42029
20. V. Totik, Weighted Approximation with Varying Weight, Lect. Notes in Math. vol. 1569, Springer-Verlag, Berlin, 1994. MR 96f:41002
21. V. Totik, Fast decreasing polynomials via potentials, J. Anal. Math. 62 (1994), 131-154. MR 96e:41010