Spectral properties of Neumann Laplacian of horns |
| |
| Authors: | E B Davies B Simon |
| |
| Institution: | (1) Department of Mathematics, King's College, Strand, WC2R 2LS London, England;(2) Division of Physics, Mathematics & Astronomy, California Institute of Technology, 253-37, 91125 Pasadena, CA, USA |
| |
| Abstract: | We study the Neumann Laplacian of unbounded regions in 
n
with cusps at infinity so that the corresponding Dirichlet Laplacian has compact resolvent. Typical of our results is that of the region {(x, y) 2 x, y|<1} the Neumann Laplacian has absolutely continuous spectrum 0,  ) of uniform multiplicity four and an infinity of eigenvaluesE
o<E
1 ...  and that for the region {(x, y)2y|1}, it has absolutely continuous spectrum 1/4, ) of uniform multiplicity 2 and an infinity of eigenvaluesE
0=0<E
1.... We use the Enss theory with a suitable asymptotic dynamics.The second author's research is partially funded under NSF grand number DMS-8801918 |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
