On certain extremal problems concerning polynomials
β Scribed by Ying-Guang Shi
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 381 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The L m extremal polynomials in an explicit form with respect to the weights (1&x) &1Γ2 (1+x) (m&1)Γ2 and (1&x) (m&1)Γ2 (1+x) &1Γ2 for even m are given. Also, an explicit representation for the Cotes numbers of the corresponding Tura n quadrature formulas and their asymptotic behavior is provided. 1
If P is a continuous m-homogeneous polynomial on a real normed space and P 8 is the associated symmetric m-linear form, the ratio &P 8 &Γ&P& always lies between 1 and m m Γm!. We show that, as in the complex case investigated by Sarantopoulos (1987, Proc. Amer. Math. Soc. 99, 340 346), there are P '