On the best convergence of trigonometric integrals (Q2565300)

The author studies the question whether \[ \inf_{g_\sigma(x)\in B_{\sigma;p}} |\psi(x)-g_\sigma(x) |_{L_p(\mathbb{R})}= \Biggl|\psi(x)-\int^\sigma_{-\sigma} F(t)\exp(itx)dt \Biggr|_{L_p(\mathbb{R})}, \] where \(B_{\sigma;p}\) is the space of entire functions of exponential type not greater than \(\sigma\geq 0\) and integrable on \(\mathbb{R}\) with the power \(p\), \(p\geq 1\). He proves three interesting theorems, but they need a lot of notations and notions, and hence it is not possible for the reviewer to recall them succinctly. The paper is worth for reading.