On the completeness of root subspaces of boundary value problems for first order systems of ordinary differential equations
By M. Malamud, L. Oridoroga. 2012
59 citations recorded by the source corpus.
The paper is concerned with the completeness problem of root functions of general boundary value problems for first order systems of ordinary differential equations. We introduce and investigate the class of weakly regular boundary conditions. We show that this class is much broader than the class of regular boundary conditions introduced by G.D. Birkhoff and R.E. Langer. Our main result states that the system of root functions of a boundary value problem is complete and minimal provided that the boundary conditions are weakly regular. Moreover, we show that in some cases the weak regularity of boundary conditions is also necessary for the completeness. Also we investigate the completeness for 2×2 Dirac type equations subject to irregular boundary conditions. Emphasize that our results are the first results on the completeness for general first order systems even in the case of regular boundary conditions.
Subfields: Computational Theory and Mathematics, Mathematical Physics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/91ec29cefa5683228b1c9786a8b4ce67aec62c6a
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In Computational Theory and Mathematics
In Mathematical Physics
In Numerical Analysis
Citations in the corpus
- Completeness and spectral synthesis of nonselfadjoint one-dimensional perturbations of selfadjoint operators (2012, methodology): “We will mention here the works by Malamud (2008), Rykhlov (2009), Shkalikov (1976, 1979, 1982) and Malamud and Oridoroga [54] (2012) (see the references in [54], where an up-to-date account of this work is given), and also the works by Minkin [64] and by Shubov [74].”
- Dirac operator with complex-valued summable potential (2014, unknown): “Из последних работ об обыкновеннных дифференциальных операторах, порождаемых матрицей n × n, отметим работы Маламуда, Оридороги и Лунева [26, 27].”