The szegö curve, zero distribution and weighted approximation

Transactions of the American Mathematical Society

Volumn 349, Issue 10, 1997, Pages 4085-4105

  Pritsker, Igor E ^a   Varga, Richard S ^a  

^a KENT STATE UNIVERSITY   (United States)

Author keywords

Balayage; Extremal measure; Logarithmic potential; Modified robin constant; Szeg curve; Weighted energy problem; Weighted polynomials

Indexed keywords

EID: 21944441945     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-97-01889-8     Document Type: Article

References (14)

1. P. B. Bonvein and W. Chen, Incomplete rational approximation in the complex plane, Constr. Approx. 11 (1995), 85-106. MR 95k:41024
2. J. D. Buckholtz, A characterization of the exponential series, Amer. Math. Monthly 73, Part II (1966), 121-123. MR 34:2838
3. z .II, Computational Methods and Function Theory, Lecture Notes in Math., vol. 1435, pp. 201-207, Springer-Verlag, Heidelberg, 1990. MR 92m:33004
4. A. J. Carpenter, R. S. Varga and J. Waldvogel, Asymptotics for the zeros of the partial sums ofez. I., Rocky Mount. J. of Math. 21 (1991), 99-119. MR 92m:33003
5. D. Gaier, Lectures on Complex Approximation, Birkhäuser, Boston, 1987. MR 88i:30059b
6. P. Henrici, Applied and Computational Complex Analysis, vol. 2, John Wiley and Sons, New York, 1977. MR 56:12235
7. N. S. Landkof, Foundations of Modern Potential Theory, Springer-Verlag, Berlin, 1972. MR 50:2520
8. G. G. Lorentz, Approximation by incomplete polynomials (problems and results), Fade and Rational Approximations: Theory and Applications (E. B. Saff and R. S. Varga, eds.), pp. 289-302, Academic Press, New York, 1977. MR 57:6956
9. H. N. Mhaskar and E. B. Saff, The distribution of zeros of asymptotically extremal polynomials, J. Approx. Theory 65 (1991), 279-300. MR 92d:30005
10. H. N. Mhaskar and E. B. Saff, Weighted analogues of capacity, transfinite diameter and Chebyshev constant, Constr. Approx. 8 (1992), 105-124. MR 93a:31004
11. E. B. Saff and V. Totik, Logarithmic Potentials with External Fields, Springer-Verlag, Heidelberg, 1997.
12. G. Szegö, Über eine Eigenshaft der Exponentialreihe, Sitzungsber. Berl. Math. Ges. 23 (1924), 50-64.
13. V. Totik, Weighted Approximation with Varying Weight, Lecture Notes in Math., vol. 1569, Springer-Verlag, Heidelberg, 1994. MR 06f:41002
14. J. L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, Colloquium Publications, vol. 20, Amer. Math. Soc., Providence, 1969. MR 36:1572b (earlier ed.)