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 , 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 467e09d9a2f343bb1f909242af5"> and (counted according to multiplicity) and one eigenvalue 46b326ac5a65f85b6e25e"> corresponding to the boundary condition (bc). We prove that the smoothness of the potential could be characterized by the decay rate of the sequence 6ea0ea1b57c4faaed053">, where 46165be391bb6ecf0c7039c"> and . 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.