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The Basis Property of Root Vectors of Loaded Second - Order Differential Operators on an Interval
- Publisher
- Springer Journals
- Copyright
- Copyright © 2016 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S0012266116120041
- Publisher site
- See Article on Publisher Site
Abstract
We consider a second-order differential operator on an interval of the real line with integral boundary conditions. We show how to construct the adjoint operator. The differential operation of the adjoint operator can be loaded, and the domain of that operator can contain functions that, together with their derivatives, have jump discontinuities at countably many points. For the root functions of the adjoint operator, we obtain integral representations, in particular, a mean-value formula.
Journal
Differential Equations – Springer Journals
Published: Jan 20, 2017