Approximation by weighted polynomials

@article{Benko2003ApproximationBW,
  title={Approximation by weighted polynomials},
  author={David Benko},
  journal={Journal of Approximation Theory},
  year={2003},
  volume={120},
  pages={153-182}
}
It is proven that if xQ′(x) is increasing on (0,+∞) and w(x) = exp(−Q) is the corresponding weight on [0,+∞), then every continuous function that vanishes outside the support of the extremal measure associated with w can be uniformly approximated by weighted polynomials of the form wPn. This problem was raised by V. Totik, who proved a similar result (the Borwein-Saff conjecture) for convex Q. A general criterion is introduced, too, which guarantees that the support of the extremal measure is… CONTINUE READING

From This Paper

Topics from this paper.
5 Citations
7 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-7 of 7 references

Weighted polynomial approximation for convex external fields

  • V. Totik
  • Constr. Approx
  • 2000
Highly Influential
4 Excerpts

Logarithmic potentials with external fields

  • E. B. Saff, V. Totik
  • Appendix B by T. Bloom. Grundlehren der…
  • 1997
Highly Influential
10 Excerpts

A note on weighted polynomial approximation with varying weights

  • A.B.J. Kuijlaars
  • J. Approx. Theory,
  • 1996
Highly Influential
9 Excerpts

The role of the endpoint in weighted polynomial approximation with varying weights

  • A.B.J. Kuijlaars
  • Constr. Approx.,
  • 1996
Highly Influential
4 Excerpts

Weighted approximation with varying weights

  • V. Totik
  • Lecture Notes in Mathematics,
  • 1994
1 Excerpt

Saff : ” Strong asymptotics for extremal polynomials associated with weights on R ”

  • B. E.
  • Lecture Notes in Mathematics
  • 1988

Strong asymptotics for extremal polynomials associated with weights on R

  • D. S. Lubinsky, E. B. Saff
  • Lecture Notes in Mathematics,
  • 1988
1 Excerpt

Similar Papers

Loading similar papers…