Hostname: page-component-5c6d5d7d68-wtssw Total loading time: 0 Render date: 2024-08-15T11:54:29.879Z Has data issue: false hasContentIssue false
  • English
  • Français

Weighted Polynomial Approximation of Entire Functions on Unbounded Subsets of the Complex Plane

Published online by Cambridge University Press:  20 November 2018

H. N. Mhaskar
H. N. Mhaskar*
Affiliation:
Department of Mathematics California State University Los Angeles, California 90032 U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the asymptotic behavior of the n-widths of a class of entire functions in weighted approximation on subsets of the complex plane.

Keywords

41A4630D99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 3 , 01 September 1993 , pp. 303 - 313
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. DeVore, R., Howard, R. and Micchelli, C. A., Optimal nonlinear approximation, Manuscripta Mathematica 63(1989), 469–478.Google Scholar
2. Mhaskar, H. N., Weighted polynomial approximation of entire functions, I, J. Approx. Theory 35(1982), 203–213.Google Scholar
3. Mhaskar, H. N., Weighted polynomial approximation of entire functions, II, J. Approx. Theory 33(1981), 59–68.Google Scholar
4. Mhaskar, H. N., Finite-infinite range inequalities in the complex plane, Internat. J. Math, and Math. Sci. 14(1991), 625–638.Google Scholar
5. Mhaskar, H. N., Weighted polynomials, radial basis functions and potentials in locally compact spaces, Num. Funct. Anal, and Opt. (9 and 10) 11(1990-91), 987–1017.Google Scholar
6. Mhaskar, H. N. and Micchelli, C. A., On the n-widthfor weighted approximation of entire functions. In: Approximation Theory VI, (eds. Chui et al.), Academic Press, New York, 1989,429–432.Google Scholar
7. Mhaskar, H. N. and Saff, E. B., Weighted analogues of capacity, transfinite diameter and Chebyshev constant, Const. Approx. 8(1992), 105–124.Google Scholar
8. Mhaskar, H. N. and Saff, E. B., The distribution of zeros of asymptotically extremal polynomials, J. Approx. Theory 65(1991), 279–300.Google Scholar
9. Mhaskar, H. N. and Saff, E. B., Extremal problems for polynomials with exponential weights, Trans. Amer. Math. Soc. 283(1984), 203–234.Google Scholar
10. Pinkus, A., n-widths in approximation theory, Springer Verlag, New York, 1985.Google Scholar
11. Saff, E. B., Orthogonal polynomials from a complex perspective. In: Orthogonal Polynomials, Theory and Practice, (ed. P. Nevai), Kluwer Academic Publ., Dordrecht, 1990, 363-393.Google Scholar
12. Tsuji, M., Potential theory in modern function theory, 2nd éd., Chelsea, New York, 1958.Google Scholar
13. Walsh, J. L., Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc, Colloq. Publ. 20, Amer. Math. Soc, Providence, R.I., 1969.Google Scholar