Essential $\mathcal{F}$-sets of $\mathbb{N}$ under nonhomogeneous spectra

Pintu Debnath

Let $\alpha >0$ and $0<\gamma <1$. Define $g_{\alpha ,\gamma }:\mathbb{N}\to \mathbb{N}$ by $g_{\alpha ,\gamma }\left(n\right)=\lfloor \alpha n+\gamma \rfloor$. The set $\left\{ g_{α,γ}\left(n\right):n\in\mathbb{N}\right\}…