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Can anyone suggest me some books or papers that include details about spectral theory on Hyperbolic spaces or related topics such as scattering theory on Hyperbolic spaces?

After some googling, I can only find papers by Jean-Philippe Anker and Vittoria Pierfelice about Schrodinger equations on Hyperbolic spaces, see e.g. http://arxiv.org/abs/0801.3523. I hope to find some references that contain more basic theory on Hyperbolic space, such as the spectral theory of Laplacian on $\mathbb{H}^n$ . Thanks in advance.

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    $\begingroup$ Scattering Theory for Automorphic Functions, by Lax and Phillips? $\endgroup$
    – Stopple
    May 29, 2015 at 4:07
  • $\begingroup$ Iwaniec's spectral theory of automorphic forms is a well-known reference (although not using representation theoretical language). One might also consider the Gelbart-Jacquet article (which is a bit advanced). If one wants to really study automorphic representations, then Bump's book or Borel's are natural starting points. $\endgroup$
    – Asaf
    May 29, 2015 at 7:38

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See http://www.mathcs.emory.edu/~davidb/spths.pdf (Introduction to Spectral Theory on Hyperbolic Surfaces, by David Borthwick) and http://link.springer.com/article/10.1007%2FBF02830802 (The geometry and spectra of hyperbolic manifolds, by Peter D. Hislop) and references therein.

This reference http://www.sciencedirect.com/science/article/pii/0370157386901596 (Chaos on the pseudosphere, by N.L. Balazs and A. Voros) might be also useful, although it is written for physicists.

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