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I have been using Barry Simon's text "Szego's Theorem and its Descendants" and Gerald Teschl's text on Jacobi matrices to learn about the theory of periodic Jacobi matrices, but I would like to have another reference on this topic.

In particular, I would like a reference which discusses the direct integral decomposition for such operators, as it is not discussed in detail in Teschl's text, and I found Simon's discussion at the end of section 5.3 on that topic to be rather confusing. This is entirely a result of my own lack of background and experience -- I don't want it to sound like I'm blaming the author.

I will be very grateful for any suggestions.

EDIT: Alternatively, I am only really confused about the proof sketch of Theorem 5.3.8 in Simon's text. In lieu of a new reference, I would be perfectly happy with an answer which clarifies the details of this sketch.

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