### On the spectra of non-selfadjoint differential operators and their adjoints in direct sum spaces.

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The general ordinary quasi-differential expression M of n-th order with complex coefficients and its formal adjoint M + are considered over a regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operator may have a finite number of singular points. By considering M over various subintervals on which singularities occur only at the ends, restrictions of the maximal operator generated by M in L2|w (a, b) which are regularly solvable with respect to the minimal operators T0 (M ) and T0...

This paper is concerned with square integrable quasi-derivatives for any solution of a general quasi-differential equation of $n$th order with complex coefficients $M\left[y\right]-\lambda wy=wf(t,{y}^{\left[0\right]},...,{y}^{[n-1]})$, $t\in [a,b)$ provided that all $r$th quasi-derivatives of solutions of $M\left[y\right]-\lambda wy=0$ and all solutions of its normal adjoint ${M}^{+}\left[z\right]-\overline{\lambda}wz=0$ are in ${L}_{w}^{2}(a,b)$ and under suitable conditions on the function $f$.

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...

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