Geodesic
Regular Ordinary Differential Operators with Involution
Matematičeskie zametki, Tome 106 (2019) no. 5, pp. 643-659

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The main results of the paper are related to the study of differential operators of the form $$ Ly = y^{(n)}(-x) + \sum_{k=1}^n p_k(x) y^{(n-k)}(-x) + \sum_{k=1}^n q_k(x) y^{(n-k)}(x),\qquad \ x\in [-1,1], $$ with boundary conditions of general form concentrated at the endpoints of a closed interval. Two equivalent definitions of the regularity of boundary conditions for the operator $L$ are given, and a theorem on the unconditional basis property with brackets of the generalized eigenfunctions of the operator $L$ in the case of regular boundary conditions is proved.
Keywords: operators with involution, regular differential operators, basis property of eigenfunctions of operators, Riesz bases. 
@article{MZM_2019_106_5_a0,
     author = {V. E. Vladykina and A. A. Shkalikov},
     title = {Regular {Ordinary} {Differential} {Operators} with {Involution}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--659},
     publisher = {mathdoc},
     volume = {106},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_5_a0/}
}
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V. E. Vladykina; A. A. Shkalikov. Regular Ordinary Differential Operators with Involution. Matematičeskie zametki, Tome 106 (2019) no. 5, pp. 643-659. http://geodesic.mathdoc.fr/item/MZM_2019_106_5_a0/