On Approximation Properties of Fourier Series in Jacobi Polynomials Orthogonal in the Sense of Sobolev.

The article deals with the problem of the deviation from a function belonging to the space of partial sums of Fourier series with respect to the system of polynomials , orthogonal with respect to an inner product of Sobolev type. Here for and where is the Jacobi polynomial of degree . The main attention is paid to obtaining an upper bound for a Lebesgue-type function of partial sums of the Fourier series with respect to the system . [ABSTRACT FROM AUTHOR]