Abstract:
We find the spectrum and prove a theorem on the expansion of an arbitrary function satisfying certain smoothness conditions in terms of the root functions of a boundary value problem of the type
\begin{gather*}
-y''+q(x)+\frac a{x^2}y=\lambda y,\quad y(0)=0,
\\
M(\lambda)y(a)+N(\lambda)y(b)=0,
\end{gather*}
where $0<a<b<\infty$, $a\ge0$, $M(\lambda)$ and $N(\lambda)$ are polynomials with complex coefficients, and $q(x)$ is a sufficiently smooth complex-valued function.
Fulltext:
PDF file (668 kB)
