Spectral and Scattering Theory

Borthwick, David

doi:10.1007/978-3-319-33877-4_7

David Borthwick⁵

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

1527 Accesses

Abstract

The basic spectral theory of the Laplacian on a geometrically finite hyperbolic manifold was worked out by Lax-Phillips [148–151], in the abstract framework of Lax-Phillips scattering theory [152].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 99.00; Price excludes VAT (USA)

Softcover Book: USD 129.99; Price excludes VAT (USA)

Hardcover Book: USD 129.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

Aronszajn, N.: A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J. Math. Pures Appl. (9) 36, 235–249 (1957)
Google Scholar
Borthwick, D.: Scattering theory for conformally compact metrics with variable curvature at infinity. J. Funct. Anal. 184, 313–376 (2001)
Article MathSciNet MATH Google Scholar
Hörmander, L.: Uniqueness theorems for second order elliptic differential equations. Commun. PDE 8, 21–64 (1983)
Article MathSciNet MATH Google Scholar
Joshi, M.S., Barreto, A.S.: Inverse scattering on asymptotically hyperbolic manifolds. Acta Math. 184, 41–86 (2000)
Article MathSciNet MATH Google Scholar
Lax, P., Phillips, R.S.: The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces. J. Funct. Anal. 46, 280–350 (1982)
Article MathSciNet MATH Google Scholar
Lax, P., Phillips, R.S.: Translation representation for automorphic solutions of the wave equation in non-Euclidean spaces. III. Commun. Pure Appl. Math. 38, 179–207 (1985)
Article MathSciNet MATH Google Scholar
Lax, P., Phillips, R.S.: Scattering Theory, 2nd edn. Academic, Boston (1989)
MATH Google Scholar
Mazzeo, R.: The Hodge cohomology of a conformally compact metric. J. Differ. Geom. 28, 309–339 (1988)
MathSciNet MATH Google Scholar
Mazzeo, R.: Unique continuation at infinity and embedded eigenvalues for asymptotically hyperbolic manifolds. Am. J. Math. 113, 25–45 (1991)
Article MathSciNet MATH Google Scholar
Melrose, R.B.: Spectral and scattering theory for the Laplacian on asymptotically Euclidian spaces. In: Spectral and Scattering Theory (Sanda, 1992). Lecture Notes in Pure and Applied Mathematics, vol. 161, pp. 85–130. Dekker, New York (1994)
Google Scholar
Melrose, R.B.: Geometric Scattering Theory. Cambridge University Press, Cambridge (1995)
MATH Google Scholar
Perry, P.A.: The Laplace operator on a hyperbolic manifold. II. Eisenstein series and the scattering matrix. J. Reine Angew. Math. 398, 67–91 (1989)
MathSciNet MATH Google Scholar

Download references

Author information

Authors and Affiliations

Department of Mathematics and Computer Science, Emory University, Atlanta, GA, USA
David Borthwick

Authors

David Borthwick
View author publications
You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Borthwick, D. (2016). Spectral and Scattering Theory. 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_7

Download citation

DOI: https://doi.org/10.1007/978-3-319-33877-4_7
Published: 13 July 2016
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-33875-0
Online ISBN: 978-3-319-33877-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

Publish with us

Policies and ethics