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I am looking for literature on entrywise invariant kernels. The specific example I have in mind is $K:R^{d}\times R^{d}\to R$ and locally compact groups acting on vector space $R^{d}$. More precisely I am looking to find properties of the eigenvectors and eigenvalues of kernels such that for any elements of the group $g,h\in R^{d\times d}$ I have $K(gx,hy)=K(x,y)$. Any suggestion? Thanks! Fabio

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  • $\begingroup$ When you refer to spectrum, what space are these kernels acting on? Could you also please be more precise on the conditions you are putting on thee kernel functions (continuity, boundedness, etc) $\endgroup$
    – Yemon Choi
    Commented Nov 20, 2020 at 21:44
  • $\begingroup$ One phrase that might be useful to look up: "Toeplitz operator" $\endgroup$
    – Yemon Choi
    Commented Nov 20, 2020 at 21:44
  • $\begingroup$ Thanks! I also edited the question to make it more clear. $\endgroup$
    – Fabio
    Commented Nov 20, 2020 at 21:50

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