Lagrange interpolation polynomials and orthogonal Fourier–Jacobi series

A. A. Privalov

Stavropol' State Pedagogical Institute

Abstract: Let $\alpha>-1$ and $\beta>-1$. Then a function $f(x)$, continuous on the segment $[-1; 1]$, exists such that the sequence of Lagrange interpolation polynomials constructed from the roots of Jacobi polynomials diverges almost everywhere on $[-1; 1]$, and, at the same time, the Fourier–Jacobi series of function $f(x)$ converges uniformly to $f(x)$ on any segment $[a; b]\subset(-1; 1)$.

UDC: 517

Received: 20.10.1975

 English version: Mathematical Notes, 1976, 20:2, 679–685

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