Wiener's problem for positive definite functions

Dmitry Gorbachev, Sergey Tikhonov

We study the sharp constant $W_n(D)$ in Wiener's inequality for positive definite functions \[ \int_{\mathbb{T}^{n}}|f|^{2}\,dx\le W_{n}(D)|D|^{-1}\int_{D}|f|^{2}\,dx,\quad D\sub…