Spectral Properties of Ordinary Differential Operators with Involution
- Authors: Vladykina V.E.1, Shkalikov A.A.1
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Affiliations:
- Faculty of Mechanics and Mathematics, Moscow State University
- Issue: Vol 99, No 1 (2019)
- Pages: 5-10
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225608
- DOI: https://doi.org/10.1134/S1064562419010046
- ID: 225608
Cite item
Abstract
Let P and Q be ordinary differential operators of order n and m generated by s boundary conditions (where s = max{n, m}) on a bounded interval [a, b]. We study operators of the form L = JP + Q, where J is an involution operator in the space L2[a, b]. Three cases are considered, namely, n > m, n < m, and n = m, for which the concepts of regular, almost regular, and normal boundary conditions are defined. Theorems on an unconditional basis property and the completeness of the root functions of the operator L depending on the type of boundary conditions from the chosen classes are announced.
About the authors
V. E. Vladykina
Faculty of Mechanics and Mathematics,Moscow State University
Author for correspondence.
Email: vika-chan@mail.ru
Russian Federation, Moscow, 119991
A. A. Shkalikov
Faculty of Mechanics and Mathematics,Moscow State University
Author for correspondence.
Email: shkalikov@mi.ras.ru
Russian Federation, Moscow, 119991