Polynomials orthogonal in the Sobolev sense, generated by Chebyshev polynomials orthogornal on a mesh

We consider the problem of constructing polynomials, orthogonal in Sobolev sense on the finite uniform mesh and associated with classical Chebyshev polynomials of discrete variable. We have found an explicit expression of these polynomials by classical Chebyshev polynomials. Also we have obtained an expansion of new polynomials by generalized powers of Newton type. We obtain expressions for the deviation of a discrete function and its finite differences from respectively partial sums of its Fourier series on the new system of polynomials and their finite differences.