On a class of operators related to second-order differential equations |
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| Authors: | N. N. Konechnaya K. A. Mirzoev |
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| Affiliation: | (1) M. V. Lomonosov Pomor State University, Lomonosova str. 4, Arkhangelsk, 163006, Russia;(2) Department of Mechanics and Mathematics, Moscow State University, Vorob’evy Gory, Moscow, 119992, Russia |
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| Abstract: | In the present paper, we find a class of linear homogeneous differential equations of order n + 1 (n > 1) whose fundamental system of solutions is constructed from the fundamental system of solutions of a second-order differential equation. The spectral properties of differential operators generated by these differential expressions are investigated. In particular, sufficient conditions are obtained for the coefficients of a second-order differential equation under which the case of maximal deficiency indices is realized. Dedicated to the memory of B. M. Levitan |
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