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Spectral properties of ordinary differential operators with involuton
- Authors: Vladykina V.E.1, Shkalikov A.A.1
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Affiliations:
- Lomonosov Moscow State University
- Issue: Vol 484, No 1 (2019)
- Pages: 12-17
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/12133
- DOI: https://doi.org/10.31857/S0869-5652484112-17
- ID: 12133
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Abstract
Let P and Q be ordinary differential operators of order n and m generated by s = max{n; m} boundary conditions on a nite interval [a; b]. We study operators of the form L = JP + Q, where J is the involution operator in the space L2[a; b]. We consider three cases n > m, n < m, and n = m, for which we dene concepts of regular, almost regular, and normal boundary conditions. We announce theorems on unconditional basis and completeness of the root functions of operator L depending on the type of boundary conditions from selected classes.
About the authors
V. E. Vladykina
Lomonosov Moscow State University
Author for correspondence.
Email: vika-chan@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991
A. A. Shkalikov
Lomonosov Moscow State University
Email: shkalikov@mi.ras.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991
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