Fourier-Sobolev Series in Continuous-Discrete Orthogonal Sobolev Polynomials

Abstract: The article studies Fourier series in continuous-discrete Sobolev spaces. The questions about the behavior of partial sums and linear means for Fourier series in orthonormal Sobolev polynomials {?̂?(?)}(?∈[−1,1]; ?∈ℤ+) are considered. Results on the convergence of Λ− summation methods uniformly and almost everywhere are obtained. The compact convergence of linear summation methods in the Sobolev spaces is studied. A consequence of the obtained results is linear summation methods for Fourier - Gegenbauer -Sobolev series in a discrete Sobolev space.