FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 4, PAGES 1199-1227

**A model of transition from discrete spectrum to continuous one in
the singular perturbation theory**

S. A. Stepin

Abstract

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```
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.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/97/974/97419t.htm

Last modified: January 27, 2000