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

O. A. Plaksina

Sbornik. Mathematics, Tome 59 (1988) no. 1, pp. 1-23

Résumé

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.