# 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 $$s_i,t_j$$.

## Related Questions

### Commutator estimates regarding pseudo-differential operators

0  Asked on December 15, 2020 by shaoyang-zhou

### English translation of Borel-Serre Le theoreme de Riemann-Roch?:

1  Asked on December 15, 2020

### Upper bound for an exponential sum involving characters of a finite field

1  Asked on December 14, 2020 by nahila

### Euler function summation

0  Asked on December 13, 2020 by andrej-leko

### A problem about an unramified prime in a Galois extension

1  Asked on December 9, 2020 by neothecomputer

### Reference request: discretisation of probability measures on $mathbb R^d$

1  Asked on December 9, 2020 by mb2009

### Smoothness of a variety implies homological smoothness of DbCoh

0  Asked on December 8, 2020 by dbcohsmoothness

### Reference for matrices with all eigenvalues 1 or -1

1  Asked on December 7, 2020

### Characterizations of groups whose general linear representations are all trivial

1  Asked on December 7, 2020 by qsh

### Continuous time Markov chains and invariance principle

0  Asked on December 6, 2020 by sharpe

### Continuity property for Čech cohomology

0  Asked on December 6, 2020 by xindaris

### Reference request: superconformal algebras and representations

0  Asked on December 6, 2020 by winawer

### Extending rational maps of nodal curves

1  Asked on December 5, 2020 by leo-herr

### How large is the smallest ordinal larger than any “minimal ordinal parameter” for any pair of an Ordinal Turing Machine and a real?

1  Asked on December 4, 2020 by lyrically-wicked

### Almost geodesic on non complete manifolds

1  Asked on December 4, 2020 by andrea-marino

### With Khinchine’s inequality, prove Fourier basis is unconditional in $L^{p}[0,1]$ only for $p=2$

0  Asked on December 3, 2020 by eric-yan

### Kähler manifolds deformation equivalent to projective manifolds

0  Asked on December 3, 2020 by user164740

### Duality of eta product identities: a new idea?

2  Asked on December 1, 2020 by wolfgang

### Is there a CAS that can solve a given system of equations in a finite group algebra $kG$?

2  Asked on December 1, 2020 by bernhard-boehmler