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This article is cited in 10 scientific papers (total in 10 papers)
On the basis property of the system of eigenfunctions and associated functions
of a one-dimensional Dirac operator
A. M. Savchuk Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
We study a one-dimensional Dirac system on a finite interval. The potential
(a 2×2 matrix) is assumed to be complex-valued and integrable. The
boundary conditions are assumed to be regular in the sense of Birkhoff. It
is known that such an operator has a discrete spectrum and the system
{yn}∞1 of its eigenfunctions and associated functions is
a Riesz basis (possibly with brackets) in L2⊕L2. Our results
concern the basis property of this system in the spaces Lμ⊕Lμ
for μ≠2, the Sobolev spaces Wθ2⊕Wθ2
for θ∈[0,1], and the Besov spaces Bθp,q⊕Bθp,q.
Keywords:
Dirac operator, eigenfunctions and associated functions, conditional basis, Riesz basis.
Received: 26.10.2016 Revised: 19.08.2017
Citation:
A. M. Savchuk, “On the basis property of the system of eigenfunctions and associated functions
of a one-dimensional Dirac operator”, Izv. Math., 82:2 (2018), 351–376
Linking options:
https://www.mathnet.ru/eng/im8623https://doi.org/10.1070/IM8623 https://www.mathnet.ru/eng/im/v82/i2/p113
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Abstract page: | 732 | Russian version PDF: | 104 | English version PDF: | 40 | References: | 121 | First page: | 43 |
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