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- W2267999532 abstract "The one-dimensional Dirac operator with periodic potential $V=begin{pmatrix} 0 & mathcal{P}(x) mathcal{Q}(x) & 0 end{pmatrix}$, where $mathcal{P},mathcal{Q}in L^2([0,pi])$ subject to periodic, antiperiodic or a general strictly regular boundary condition $(bc)$ has discrete spectrums. It is known that, for large enough $|n|$ in the disc centered at $n$ of radius 1/4, the operator has exactly two (periodic if $n$ is even or antiperiodic if $n$ is odd) eigenvalues $lambda_n^+$ and $lambda_n^-$ (counted according to multiplicity) and one eigenvalue $mu_n^{bc}$ corresponding to the boundary condition $(bc)$. We prove that the smoothness of the potential could be characterized by the decay rate of the sequence $|delta_n^{bc}|+|gamma_n|$, where $delta_n^{bc}=mu_n^{bc}-lambda_n^+$ and $gamma_n=lambda_n^+-lambda_n^-.$ Furthermore, it is shown that the Dirac operator with periodic or antiperiodic boundary condition has the Riesz basis property if and only if $suplimits_{gamma_nneq0} frac{|delta_n^{bc}|}{|gamma_n|}$ is finite." @default.
- W2267999532 created "2016-06-24" @default.
- W2267999532 creator A5090982568 @default.
- W2267999532 date "2016-02-03" @default.
- W2267999532 modified "2023-09-27" @default.
- W2267999532 title "Characterization of the potential smoothness of one-dimensional Dirac operator subject to general boundary conditions and its Riesz basis property" @default.
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