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Spectral Theory for the Hyperbolic Plane

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Part of the book series: Progress in Mathematics ((PM,volume 318))

Abstract

In our discussion of spectral theory we naturally start with the hyperbolic plane itself, the primary example of a hyperbolic surface of infinite area.

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References

  1. Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher Transcendental Functions, vol. I. McGraw-Hill, New York/Toronto/London (1953). Based, in part, on notes left by Harry Bateman

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  2. Gaffney, M.P.: The harmonic operator for exterior differential forms. Proc. Natl. Acad. Sci. U.S.A. 37, 48–50 (1951)

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  3. Hislop, P.D.: The geometry and spectra of hyperbolic manifolds. spectral and inverse spectral theory. Proc. Indian Acad. Sci. Math. Sci. 104, 715–776 (1994)

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  4. Olver, F.W.J.: Asymptotics and Special Functions. Academic, New York/London (1974)

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Borthwick, D. (2016). Spectral Theory for the Hyperbolic Plane. In: Spectral Theory of Infinite-Area Hyperbolic Surfaces. Progress in Mathematics, vol 318. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-33877-4_4

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