Abstract:
We study a one-dimensional Dirac system on a finite interval. The potential
(a $2\times 2$ 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
$\{\mathbf{y}_n\}_1^\infty$ of its eigenfunctions and associated functions is
a Riesz basis (possibly with brackets) in $L_2\oplus L_2$. Our results
concern the basis property of this system in the spaces $L_\mu\oplus L_\mu$
for $\mu\ne2$, the Sobolev spaces ${W_2^\theta\oplus W_2^\theta}$
for $\theta\in[0,1]$, and the Besov spaces $B^\theta_{p,q}\oplus B^\theta_{p,q}$.
Keywords:Dirac operator, eigenfunctions and associated functions, conditional basis, Riesz basis.
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