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Inverse problems of spectral analysis for the Sturm–Liouville operators with nonseparated boundary conditions

O. A. Plaksina


Abstract: This paper is devoted to the study of boundary value problems generated by the Sturm–Liouville equation
$$ -y''(x)+q(x)y(x)=\lambda^2y(x) $$
on the interval $[0,\pi]$, with real potential $q(x)\in L_2[0,\pi]$ and with general selfadjoint boundary conditions
$$ a_{11}y(0)+a_{12}y'(0)+a_{13}y(\pi)+a_{14}y'(\pi)=0,\quad a_{21}y(0)+a_{22}y'(0)+a_{23}y(\pi)+a_{24}y'(\pi)=0. $$

For all such problems a characterization of the spectrum is found, i.e. complementary spectral data which, together with the spectrum, allow one to recover the boundary value problem uniquely.
Figures: 4.
Bibliography: 18 titles.

UDC: 517.9

MSC: Primary 34B25, 34B05; Secondary 34E05, 30C20

Received: 03.10.1984 and 08.10.1985

 English version: Mathematics of the USSR-Sbornik, 1988, 59:1, 1–23

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