Behavior of Best L , Polynomial Approximants on the Unit Interval and on the Unit Circle

  title={Behavior of Best L , Polynomial Approximants on the Unit Interval and on the Unit Circle},
  author={X. Lr},
  • X. Lr
  • Published 2003
For function f defined on the interval I:= [-1, 11; let p2J.f) be its best approximant out of-ql under the L2 norm where dz is a finite Bore1 measure on I. We compare the L, norm of the error function f-pzz(f) on subintervals vs that on the whole interval I. Then we consider the distribution of the zeros of the best L, approximants. Corresponding results are also obtained for approximation on the unit circle {ZEC : 171 = 1). 

From This Paper

Topics from this paper.


Publications citing this paper.


Publications referenced by this paper.
Showing 1-10 of 13 references

TOTIK, X-th root asymptotic behavior of orthonormal polynomials. in “Orthogonal Polynomials: Theory and Practice (Paul Nevai, Ed.)

  • V. H. STAHL
  • Kluwer Acad. Pub.,” Dordrecht
  • 1990

SAFF AND V. TOTIK; Weighted polynomial approximation of analytic functions

  • E B.
  • J. London Muth. Sot. (21
  • 1988

SAFF. A principle of contamination in best polynomial approximation, in “Approximation and Optimization

  • E B.
  • (Gomez ef a/.: Eds.), Lecture Notes in…
  • 1988

The density of extreme points in complex pol?norziai approximation

  • A. Kti ASD E.B. SAFF
  • Proc. Amer. Math. Sot
  • 1988

Asymptotic Distribution of Zeros of Approximating Polynomials,

  • Dissertation; University of South Florida,
  • 1987

NEVA 15 ASD V . ToirK , Asymptotics of the ratio oi leading coe * Z ’ icienrs of orthonormai polynomials on the unit circie , Consrr

  • P. Miti.
  • Ante . * . J . Murh .
  • 1987

Strong and weak convergence of ortbogorel pci)-nomials, Ante.

  • A. Xr. P. XWAI, V. TOTIK
  • J. Murh
  • 1987

NEVA15 ASD V. ToirK, Asymptotic-s of the ratio oi leading coe*Z’icienrs of orthonormai polynomials on the unit circie

  • P. Miti
  • Consrr. .Cppro~
  • 1985

DcRE~‘, “Theory of H

  • P L.
  • Spaces.” Academic Press. Iicn York;
  • 1973

Similar Papers

Loading similar papers…