We propose a regularization of the formal differential expression \( \begin{array}{cc}\hfill l(y)={i}^m{y}^{(m)}(t)+q(t)y(t),\hfill & \hfill t\in \left(a,b\right)\hfill \end{array} \) , of order m ≥ 2 with matrix distribution q. It is assumed that q = Q ([m/2]), where Q = (Q i,j ) s i,j = 1 is a matrix function with entries Q i,j \( \epsilon \) L 2[a, b] if m is even and Q i,j \( \epsilon \) L 1[a, b], otherwise. In the case of a Hermitian matrix q, we describe self-adjoint, maximal dissipative, and maximal accumulative extensions of the associated minimal operator and its generalized resolvents.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 5, pp. 625–634, May, 2015.
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Konstantinov, O.O. Two-Term Differential Equations with Matrix Distributional Coefficients. Ukr Math J 67, 711–722 (2015). https://doi.org/10.1007/s11253-015-1109-x
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DOI: https://doi.org/10.1007/s11253-015-1109-x