We consider a Sturm-Liouville operator with boundary conditions rationally dependent on the eigenparameter. We study the basis property in $L_p$ of the system of eigenfunctions corresponding to this operator. We determine the explicit form of the biorthogonal system. Using this we establish a theorem on the minimality of the part of the system of eigenfunctions. For the basisness in L₂ we prove that the system of eigenfunctions is quadratically close to trigonometric systems. For the basisness in $L_p$...

In this paper, the general ordinary quasi-differential expression $M_p$ of $n$-th order with complex coefficients and its formal adjoint $M_p^{+}$ on any finite number of intervals $I_p=(a_p,b_p)$, $p=1,\cdots ,N$, are considered in the setting of the direct sums of $L_{w_p}^2(a_p,b_p)$-spaces of functions defined on each of the separate intervals, and a number of results concerning the location of the point spectra and the regularity fields of general differential operators generated by such expressions are obtained. Some of these are extensions or generalizations...