论文标题
真实线上无质量狄拉克操作员的逆共振散射
Inverse resonance scattering for massless Dirac operators on the real line
论文作者
论文摘要
我们认为具有紧凑型电势的真实线路上的无质量狄拉克操作员。我们解决了两个逆问题（包括表征）：就反射系数的零和反射系数（即共振）而言。我们证明，潜力是由反射系数的零唯一决定的，并且具有相同共振的不同潜力。我们描述了一组“同耐潜力”。此外，我们证明了以下内容： 1）可以任意移动反射系数的零，以便我们获得其他紧凑型电势的反射系数零的序列， 2）估计有共振的禁止域， 3）确定共振函数的渐近学， 4）这些结果应用于规范系统。
We consider massless Dirac operators on the real line with compactly supported potentials. We solve two inverse problems (including characterization): in terms of zeros of reflection coefficient and in terms of poles of reflection coefficients (i.e. resonances). We prove that a potential is uniquely determined by zeros of reflection coefficients and there exist distinct potentials with the same resonances. We describe the set of "isoresonance potentials". Moreover, we prove the following: 1) a zero of the reflection coefficient can be arbitrarily shifted, such that we obtain the sequence of zeros of the reflection coefficient for an other compactly supported potential, 2) the forbidden domain for resonances is estimated, 3) asymptotics of resonances counting function is determined, 4) these results are applied to canonical systems.
