刊名:Journal of Mathematical Analysis and Applications
出版年:2017
出版时间:1 March 2017
年:2017
卷:447
期:1
页码:84-108
全文大小:472 K
文摘
The one-dimensional Dirac operator with periodic potential bb05b520c17ce6a153c">, where P,Q∈L2([0,π]) subject to periodic, antiperiodic or a general strictly regular boundary condition (bc ), has discrete spectrums. It is known that, for large enough e551fefb5817d04b7dda594a" title="Click to view the MathML source">|n| in the disk centered at n of radius 1/2, the operator has exactly two (periodic if n is even or antiperiodic if n is odd) eigenvalues bb1f909242af5"> and (counted according to multiplicity) and one eigenvalue corresponding to the boundary condition e4" title="Click to view the MathML source">(bc). We prove that the smoothness of the potential could be characterized by the decay rate of the sequence , where e46165be391bb6ecf0c7039c"> and bb36cf1cfc1a6a5642226307f24bbde">98" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16305844-si10.gif">. Furthermore, it is shown that the Dirac operator with periodic or antiperiodic boundary condition has the Riesz basis property if and only if is finite.