Let $T \in\left(0,1\right)$, $n\in\mathbb{N}$ and $e_n = [1,\ldots,1]\in\mathbb{R}^n$. Consider the covariance matrix $\mathfrak{A}_n = \left[sinc\left(\frac{T\left(r-s\right)}{n}\right)\right]^n_{r,s=1}\in\mathbb{R}^{n\times n}$ in which $sinc(x) = \frac{\sin\left(x\right)}{x}$. How can we prove that for large enough $n$, there is a universal constant $M > 0$ such that
\begin{equation} e^T_n\mathfrak{A}^{-1}_ne_n \leq M \end{equation}
So, the sum of the entries of $\mathfrak{A}^{-1}_n$ is bounded. My simulation shows that the above inequality is valid. I've tried to use the following result to overcome the lack of knowledge about $\mathfrak{A}^{-1}_n$.
For any $w\in\mathbb{R}^n$ and any positive definite (invertible) matrix, $\Sigma\in\mathbb{R}^{n\times n}$,
\begin{equation*} w^T \Sigma^{-1}w = \frac{1}{\min_{v^Tw = 1} v^T\Sigma v} \end{equation*}