Geodesic
Spectral Theory for the Neumann Laplacian on Planar Domains With Horn-Like Ends
Canadian journal of mathematics, Tome 49 (1997) no. 2, pp. 232-262

Voir la notice de l'article provenant de la source Cambridge University Press

The spectral theory for the Neumann Laplacian on planar domains with symmetric, horn-like ends is studied. For a large class of such domains, it is proven that the Neumann Laplacian has no singular continuous spectrum, and that the pure point spectrum consists of eigenvalues of finite multiplicity which can accumulate only at 0 or ∞. The proof uses Mourre theory.
DOI : 10.4153/CJM-1997-012-8
Mots-clés : 35P25, 58G25 
Edward, Julian. Spectral Theory for the Neumann Laplacian on Planar Domains With Horn-Like Ends. Canadian journal of mathematics, Tome 49 (1997) no. 2, pp. 232-262. doi: 10.4153/CJM-1997-012-8
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[1] 1. Berger, G., Asymptotische Eigenwertverteilung des Laplace-Operators in bestimmten unbeschrankten Gebieten mit Neumannschen Randbedingungen und Restgliedabschatzungen, Z. Anal. Anwendungen 4(1985), 85–96. Google Scholar

[2] 2. Cycon, H.L., Froese, R.G., Kirsch, W., and Simon, B., Schrodinger Operators, with Applications to Spectral Geometry, Springer Texts and Monographs in Physics, Springer-Verlag, Berlin, 1987. Google Scholar

[3] 3. Davies, E.B. and Simon, B., Spectral properties of the Neumann Laplacian on horns, Geom. Funct. Anal. (1) 2(1992), 105–117. Google Scholar

[4] 4. Edward, J., Spectral theory of the Neumann Laplacian on asymptotically perturbed waveguides, submitted. Google Scholar

[5] 5. Evans, W.D. and Harris, D.J., Sobolev embeddings for generalised ridge domains, Proc. London Math. Soc. (3) 54(1987), 141–175. Google Scholar

[6] 6. Froese, R.G. and Hislop, P., Spectral analysis of second order elliptic operators on non-compact manifolds, Duke Math. J. 58(1989), 103–129. Google Scholar

[7] 7. Hempel, R., Seco, L., and Simon, B., The essential spectrum of Neumann Laplacians on some bounded singular domains, J. Funct. Anal. 102(1991), 448–483. Google Scholar

[8] 8. Jaksic, V., On the Spectrum of Neumann Laplacian of Long Range Horns: A note on Davies-Simon Theorem, Proc. Amer.Math. Soc. 119(1993), 663–669. Google Scholar

[9] 9. Jaksic, V., Molcanov, S., and Simon, B., Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps, J. Funct. Anal. (1) 106(1992), 59–79. Google Scholar

[10] 10. Mourre, E., Absence of singular continuous spectrum for certain self-adjoint operators, Comm. Math. Phys. 78(1981), 391–408. Google Scholar

[11] 11. Reed, M. and Simon, B., Methods of Modern Mathematical Physics, Vols. 1–4. New York, Academic Press, 1972. Google Scholar

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