An extremal problem for algebraic polynomials in the symmetric discrete Gegenbauer-Sobolev space

We study discrete Sobolev spaces with symmetric inner product [Graphics] is the Gegenbauer probability measure. We obtain the solution of the following external problem: Calculate [Graphics] where the a(j)(0), j = N - r + 1 N - r + 2 , ... , N - 1, N, a(N)(0) > 0, are fixed numbers, and find the extremal polynomial.