Equilibrium problems associated with fast decreasing polynomials

Proceedings of the American Mathematical Society

Volumn 127, Issue 4, 1999, Pages 1065-1074

  Kuijlaars, A B J ^a   Dragnev, P D ^b,c  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b UNIVERSITY OF SOUTH FLORIDA   (United States)

^c INDIANA UNIVERSITY PURDUE UNIVERSITY FORT WAYNE   (United States)

Author keywords

Balayage; Equilibrium measures; Extremal support; Fast decreasing polynomials

Indexed keywords

EID: 22644450485     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-99-04590-6     Document Type: Article

References (19)

1. P.D. Dragnev, Constrained energy problems for logarithmic potentials, Ph.D. Thesis, University of South Florida, Tampa, FL, 1997.
2. P.D. Dragnev and E.B. Saff, Constrained energy problems with applications to orthogonal polynomials of a discrete variable, J. Anal. Math. 72 (1997), 223-259. CMP 98:04
3. F.D. Gakhov, Boundary Value Problems, Pergamon Press, Oxford, 1966. MR 33:6311
4. A.A. Gonchar and E.A. Rakhmanov, Equilibrium measure and the distribution of zeros of extremal polynomials, Mat. Sb. 125 (1984), 117-127 (Russian).
5. English transi, in Math. USSR Sb. 53 (1986), 119-130. MR 86f:41002
6. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, Orlando, 1980. MR 81g:33001
7. K.G. Ivanov and V. Totik, Fast decreasing polynomials, Constr. Approx. 6 (1990), 1-20. MR 90k:2G023
8. A.B.J. Kuijlaars and W. Van Assche, A problem of Totik on fast decreasing polynomials, Constr. Approx. 14 (1998), 97-112. CMP 98:05
9. _, A contact problem in elasticity related to weighted polynomials on the real line, Rend. Circ. Mat. Palermo Suppl. 52 (1998), 575-587.
10. N.S. Landkof, Foundations of Modern Potential Theory, Springer-Verlag, New York, 1972. MR 50:2520
11. D.S. Lubinsky and E.B. Saff, Strong Asymptotics for Extremal Polynomials Associated with Weights on R, Lecture Notes Math., vol. 1305, Springer-Verlag, New York, 1988. MR 89m:41013
12. D.S. Lubinsky and V. Totik, How to discretize a logarithmic potential?, Acta Sei. Math. (Szeged) 57 (1993), 419-428.
13. H.N. Mhaskar and E.B. Saff, Extremal problems for polynomials with exponential weights, Trans. Amer. Math. Soc. 285 (1984), 203-234. MR 86b:41024
14. N.I. Muskhelishvili, Singular Integral Equations, Noordhoff, Groningen, 1953. MR 15:434e
15. E.B. Saff and V. Totik, Logarithmic Potentials with External Fields, Springer-Verlag, Berlin, 1997.
16. H. Stahl and V. Totik, General Orthogonal Polynomials, Cambridge University Press, Cambridge, 1992.
17. V. Totik, Fast decreasing polynomials via potentials, J. Anal. Math. 62 (1994), 131-154. MR 96e:41010
18. _, Weighted Approximation with Varying Weight, Lecture Notes Math., vol. 1569, Springer-Verlag, Berlin, 1994. MR 96f:41002
19. _, Problem 13.5, in: Linear and Complex Analysis Problem Book 3, Part II (V.P. Havin and N.K. Nikolski, eds.), Lecture Notes Math., vol. 1574, Springer-Verlag, Berlin, 1994.