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

The purpose of this paper is to show regularity of (0, 1, ..., r − 2, r) and (0, 1, ..., r − 2, r)* interpolations on the sets obtained by projecting vertically the zeros of (1 − x2)P(α,β)n(x) (− 1) < α,β ≤ 12), (1 − x2)P(α,β)n(x) (− 1 < α ≤ 12, − 1 < β ≤ −12) and (1 + x) P(α,β)n(x) (− 1 < α ≤ −12, − 1 < β ≤ 12) respectively onto the unit circle, where P(α,β)n(x) stands for the nth Jacobi polynomial.