Nongeometric convergence of best $L_ p\ (p\neq 2)$ polynomial approximants
HTML articles powered by AMS MathViewer
- by K. G. Ivanov and E. B. Saff
- Proc. Amer. Math. Soc. 110 (1990), 377-382
- DOI: https://doi.org/10.1090/S0002-9939-1990-1019751-7
- PDF | Request permission
Abstract:
For an arbitrary function $f$ analytic in the disk $D:\left | z \right | < 1$ and continuous in $\bar D$, we show that geometric convergence in $D$ of best ${L_p}(1 \leq p \leq \infty )$ polynomial approximants to $f$ on $C:\left | z \right | = 1$ is assured only when $p = 2$.References
- E. B. Saff and V. Totik, Behavior of polynomials of best uniform approximation, Trans. Amer. Math. Soc. 316 (1989), no. 2, 567–593. MR 961628, DOI 10.1090/S0002-9947-1989-0961628-3
- J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 377-382
- MSC: Primary 41A10; Secondary 41A50, 41A63
- DOI: https://doi.org/10.1090/S0002-9939-1990-1019751-7
- MathSciNet review: 1019751