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Regular and completely regular differential operators. (English. Russian original) Zbl 1156.34075
Math. Notes 81, No. 4, 566-570 (2007); translation from Mat. Zametki 81, No. 4, 636-640 (2007).
In the space \(L_2(0,1),\) the authors consider the operator \(L\) generated by the differential expression
\[ l(y) = (-i)^n y^{(n)}(x) + p_2(x)y^{(n-2)} + \dots + p_n(x) y \] and \(n\) linearly independent boundary conditions of the form
\[ U_j(y) = \sum_{s=0}^{n-1}(a_{j,s}y^{(s)}(0) + b_{j,s}y^{(s)}(1)) = 0,\quad j = 1,\dots ,n. \] Several sufficient and necessary conditions for Birkhoff regularity and complete regularity of the operator \(L\) are obtained.

MSC:
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
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