×

Estimate of the coefficients of a generalized Fourier-Legendre series. (Russian) Zbl 0779.42015

Let \(f\) be a function of bounded variation on [0,1], \(F(x):=\int^ x_ 0f(t)dt\), and \(a_ n\) the \(n\)th Fourier coefficient of \(F\) with respect to the Legendre quasipolynomials \(\{P_ n(x):n\geq 0\}\). The author proves an estimate on \(a_ n\), whence he deduces the absolute and uniform convergence of the expansion of \(F\) with respect to \(\{P_ n\}\) on every interval inside (0,1).
Reviewer: F.Móricz (Szeged)

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
PDFBibTeX XMLCite