There are a couple errors on pages 21-22. Propositions 1.8 and 1.10 are not correctly stated; a counterexample to both is

The bound needed on in Proposition 1.8 is stronger: . Along the same lines, the bound needed on in Proposition 1.10 is .

With these modifications, the proofs alluded to after each proposition do work. I suggest also changing to $x_1, x_{1+k}, x_{1+2k}, \ldots$ on page 21 and removing the variable from Proposition 1.10.

]]>.

*Proof*

too short to write

in a comment.

]]>

And thus, if you treat as a local expert,

]]>For the positive definite imaginary part, I am still a bit confused. The imaginary part of does not even seem to be Hermitian. But I think I see how to get the conclusion that follows anyway: The eigenvalues above have positive imaginary part . Using the fact that has an orthogonal eigenbasis, you can now calculate that the has a nonnegative imaginary part for any .

Is this what it means for the imaginary part of $\latex R$ to be positive definite?

]]>For the positive definite imaginary part, I am still a bit confused. The imaginary part of does not even seem to be Hermitian. But I think I see how to get the conclusion that follows anyway: The eigenvalues above have positive imaginary part . Using the fact that has an orthogonal eigenbasis, you can now calculate that the has a nonnegative imaginary part for any .

Is this what it means for the imaginary part of $\latex R$ to be positive definite?

]]>$latex[x^2 + \phi]$ ]]>