On the Relation between the S-matrix and the Spectrum of the Interior Laplacian

A. G. Ramm. "On the Relation between the S-matrix and the Spectrum of the Interior Laplacian." Bulletin of the Polish Academy of Sciences. Mathematics 57.2 (2009): 181-188. <http://eudml.org/doc/281147>.

@article{A2009,
abstract = {The main results of this paper are: 1) a proof that a necessary condition for 1 to be an eigenvalue of the S-matrix is real analyticity of the boundary of the obstacle, 2) a short proof that if 1 is an eigenvalue of the S-matrix, then k² is an eigenvalue of the Laplacian of the interior problem, and that in this case there exists a solution to the interior Dirichlet problem for the Laplacian, which admits an analytic continuation to the whole space ℝ³ as an entire function.},
author = {A. G. Ramm},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
language = {eng},
number = {2},
pages = {181-188},
title = {On the Relation between the S-matrix and the Spectrum of the Interior Laplacian},
url = {http://eudml.org/doc/281147},
volume = {57},
year = {2009},
}

TY - JOUR
AU - A. G. Ramm
TI - On the Relation between the S-matrix and the Spectrum of the Interior Laplacian
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2009
VL - 57
IS - 2
SP - 181
EP - 188
AB - The main results of this paper are: 1) a proof that a necessary condition for 1 to be an eigenvalue of the S-matrix is real analyticity of the boundary of the obstacle, 2) a short proof that if 1 is an eigenvalue of the S-matrix, then k² is an eigenvalue of the Laplacian of the interior problem, and that in this case there exists a solution to the interior Dirichlet problem for the Laplacian, which admits an analytic continuation to the whole space ℝ³ as an entire function.
LA - eng
UR - http://eudml.org/doc/281147
ER -