Polynomials, orthogonal on non-uniform grids

Asymptotic properties of polynomials $\hat p_n(t)$, orthogonal with weight $\Delta t_j$ on any finite set of $N$ points from segment $[-1,1]$ are investigated. Namely an asymptotic formula is proved in which asymptotic behaviour of these polynomials as $n$ tends to infinity together with $N$ is closely related to asymptotic behaviour of the Lasiandra polynomials. Furthermore are investigated the approximating properties of the sums by Fourier on these polynomials.