Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-31T05:18:51.166Z Has data issue: false hasContentIssue false
  • English
  • Français

The principle of limiting absorption for Laplacians on two-point homogeneous spaces

Published online by Cambridge University Press:  14 November 2011

M. Thompson
M. Thompson
Affiliation:
Departmento de Matemática Pura e Applicada, Universidade Federal do Rio Grande do Sul, Rua Sarmento Leite 425-3°. andar, 90.000 Porto Alegre, RS, Brasil
Get access Rights & Permissions [Opens in a new window]

Synopsis

The present note is concerned to develop the principle of limiting absorption for the Laplacian Δ on a two-point homogeneous noncompact space M = G/H subject to a real-valued potential perturbation V. Such a property depends on the detailed structure of the Laplacian in a suitable coordinate system while V is assumed to satisfy a short-range condition.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 87 , Issue 3-4 , 1981 , pp. 319 - 329
Copyright
Copyright © Royal Society of Edinburgh 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Agmon, S.. Spectral properties of Schrödinger operators and scattering theory. Ann. Scuola Norm. Sup. Pisa 2 (1975), 151–218.Google Scholar
2Ju.Berezanski, M.. Expansion in Eigenfunctions of Selfadjoint Operators, Translations of Mathematical Monographs, Vol. 17 (Providence, Rhode Island; A.M.S., 1968).CrossRefGoogle Scholar
3Chernoff, P.R.. Schrödinger and Dirac operators with singular potentials and hyperbolic equations. Pacific J. Math. 72 (1977), 361–382.CrossRefGoogle Scholar
4Dunford, N. and Schwartz, J. T.. Linear Operators, Pt II (New York: Interscience, 1963).Google Scholar
5Helgason, S.. Differential operator on homogeneous spaces. Acta Math. 102 (1959), 239–299.CrossRefGoogle Scholar
6Helgason, S.. Differential Geometry and Symmetric Spaces (New York: Academic Press, 1962).Google Scholar
7Kato, T.. Perturbation for Linear Operators (Berlin: Springer, 1966).Google Scholar
8Titchmarsh, E. C.. Eigenfunction Expansions, Pt I (London: Oxford Univ. Press, 1962).Google Scholar
9Watson, G. N.. A Treatise on the Theory of Bessel Functions (London: Cambridge Univ. Press, 1966).Google Scholar