Regularity of (0, 1, ..., r − 2, r) and (0, 1, ..., r − 2, r)* Interpolations on Some Sets of the Unit Circle

✍ Scribed by S.Q. Xie

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 149 KB
• Volume: 82
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1995.1067

✦ Synopsis

The purpose of this paper is to show regularity of ((0,1, \ldots, r-2, r)) and ((0,1, \ldots, r-2, r)^{*}) interpolations on the sets obtained by projecting vertically the zeros of (\left.\left(1-x^{2}\right) P_{n}^{(\alpha, \beta)}(x)(-1)<\alpha, \beta \leqslant \frac{1}{2}\right),(1-x) P_{n}^{(\alpha, \beta)}(x) \quad\left(-1<\alpha \leqslant \frac{1}{2},-1<\right.) (\left.\beta \leqslant-\frac{1}{2}\right)) and ((1+x) P_{n}^{(\alpha, \beta)}(x)\left(-1<\alpha \leqslant-\frac{1}{2},-1<\beta \leqslant \frac{1}{2}\right)) respectively onto the unit circle, where (P_{n}^{(x, \beta)}(x)) stands for the (n)th Jacobi polynomial. 1995 Academic Press. Inc.