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I would like to know if there is a book (or a paper) which can give me an introduction to LAP. I tried to read some papers by myself, but I don't feel comfortable. I think that I need the basic ideas behind this tool. I apologize for being too vague. Thank you for any suggestions.

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    $\begingroup$ Reed-Simon discuss the topic at some length. $\endgroup$ May 26, 2015 at 17:09

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Well, there's Terence Tao's blog on this topic, you can't go wrong starting from there.

For a more extensive intro, with many references, you could take a look at this Ph.D. thesis: The Principles of Limit Absorption and Limit Amplitude for Periodic Operators

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