Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space L 2((a, b) × (c, d); p(x)q(y))

Abstract

Sharp estimates are obtained for the convergence rate of double Fourier series in terms of general orthogonal polynomials in some classes of functions and for the Kolmogorov N-widths of these classes. These results find applications in numerical analysis.