I am trying to verify and use Theorem 3.4 in this paper.
I can verify the theorem computationally in most case. However, when I apply it to a Hermitian Block Toeplitz Matrices with zero eigenvalues and pick any nascent Dirac delta function as the function F that acts on lambda, I find the equallity failed. Here are some example F I used:
f[x_List]:=(\[Epsilon]/(Pi(\[Epsilon]^2+#^2))&)/@x/.{\[Epsilon]->0.01};
f[x_List]:=100 Exp[-100(x^2)];
Am I making any mistake in the picking of these functions? I think since they decay fast enough, it is reasonably to regard them as having compact support. Or is there any other mistake I could be making?