Let $f \in L^1(\mathbb{R})$ be an integrable function which does not vanish identically and let $n,k \in \mathbb N_0$. I'm working on a problem where an infinite matrix of the following form appears: $$ A= \left ( \int_0^1 f(x)(x+k)^n \, dt \right )_{k,n \in \mathbb N_0}. $$ I.e. each entry is the integral of $f$ agains a shifted monomial, or in other words the convolution of $f$ with $x^n$ evaluated at $k$. I was wondering if such matrices are studied somewhere in the literature.
