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Eigenvalues of convolution matrices

MathOverflow Asked by Sina Baghal on January 1, 2022

Let $h: mathbb{R}to mathbb{R}$ be a smooth function. Fix $0leq s_1leq cdots leq s_mleq 1$ and $0leq t_1leq cdots leq t_nleq 1$. Construct $Ain mathbb{R}^{mtimes n}$ by letting $A_{i,j}:=h(s_i-t_j)$. What can we say about the eigenvalues of $A^TA$ and their decay rate? Assuming reasonable conditions on $s_i,t_j$.

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