On linear summability methods of fourier series in polynomials orthogonal in a discrete Sobolev space

Under study are the discrete Sobolev spaces with the inner product
\begin{align*} \int^1_{-1}f(x)g(x)w(x)\,dx&+A_1f(1)g(1)\\ &+B_1f(-1)g(-1)+A_2f'(1)g'(1)+B_2f'(-1)g'(-1)=\langle f,g\rangle. \end{align*}
Some results are presented on linear summation methods for Fourier series in orthonormal polynomials of discrete Sobolev spaces.