Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 4, pp. 1199-1227
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S. A. Stepin. A model of transition from discrete spectrum to continuous one in the singular perturbation theory. Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 4, pp. 1199-1227. http://geodesic.mathdoc.fr/item/FPM_1997_3_4_a18/
@article{FPM_1997_3_4_a18,
author = {S. A. Stepin},
title = {A~model of transition from discrete spectrum to continuous one in the singular perturbation theory},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {1199--1227},
year = {1997},
volume = {3},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1997_3_4_a18/}
}
TY - JOUR
AU - S. A. Stepin
TI - A model of transition from discrete spectrum to continuous one in the singular perturbation theory
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 1997
SP - 1199
EP - 1227
VL - 3
IS - 4
UR - http://geodesic.mathdoc.fr/item/FPM_1997_3_4_a18/
LA - ru
ID - FPM_1997_3_4_a18
ER -
%0 Journal Article
%A S. A. Stepin
%T A model of transition from discrete spectrum to continuous one in the singular perturbation theory
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1997
%P 1199-1227
%V 3
%N 4
%U http://geodesic.mathdoc.fr/item/FPM_1997_3_4_a18/
%G ru
%F FPM_1997_3_4_a18
The spectral problem \begin{gather*} i\varepsilon y''(x)+(x-\lambda)y(x)=0, \\ y(-1)=y(1)=0 \end{gather*} is considered where $\lambda$ is a spectral parameter and $\varepsilon>0$ is a small parameter. Spectrum localization, behavior of eigenfunctions and Green function of this problem are studied by analytical means.
