The approximative properties of the truncated Fourier series and the interpolational Lagrange polynomials in the spaces $L_{p,p}, ρ(x) = (1 + x^2)^{-1}, p > 1,$ and $L_p, p ≥ 2$ on the real axis by the special systems of functions, are determined. The sufficient conditions of convergence of the interpolational Lagrange polynomials and the truncated Fourier series depending on structural properties of the approximated functions, are obtained.

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