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 20c17ce6a153c">, 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 |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 and c305904ecec99c24a8c727f639170d95"> (counted according to multiplicity) and one eigenvalue corresponding to the boundary condition (bc). We prove that the smoothness of the potential could be characterized by the decay rate of the sequence , where 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.