Spectrum of weighted Birkhoff average

Balázs Bárány, Michał Rams, Ruxi Shi

Let $\{s_n{\}}_{n\in \mathbb{N}}$ be a decreasing nonsummable sequence of positive reals. In this paper, we investigate the weighted Birkhoff average $\frac{1}{S_n}{\sum }_{k=0}^{n-1}{s}_k\varphi (T^{k}x)$…