已知部分势函数的AKNS算子的逆谱问题
|
摘要
考虑定义在[0,1]区间上AKNS算子的逆谱问题。证明了假设2组势函数在区间■上已知且它们的差属于L~p空间,若2个系统的共同特征值的数量足够大则这2组势函数相等,且共同特征值的数量与系数p和a有关。
We consider the AKNS systems on the interval[0,1] and prove that two potentials already known on ■ and their difference in L~p are equal if the number of their common eigenvalues is sufficiently large. The result here is to write down explicitly this number in terms of p(and a) showing the role of p.
We consider the AKNS systems on the interval[0,1] and prove that two potentials already known on ■ and their difference in L~p are equal if the number of their common eigenvalues is sufficiently large. The result here is to write down explicitly this number in terms of p(and a) showing the role of p.
引文
[1] AMOUR L.Inverse spectral theory for the AKNS system with separated boundary conditions[J].Inverse Problems,1993,9:507-523.
[2] WATSON B A.Inverse spectral problems for weighted Dirac systems[J].Inverse Problem,1999,15(3):793-80.
[3] GASYMOV M G,LEVITAN B M.Determining the Dirac system from scattering phase[J].Dokl Akad Nauk SSSR,1996,167:1219-1222.
[4] LEVITAN B M,SARGSJAN I S.Sturm-Liouville and Dirac operators[M].Berlin:Spriger,1988.
[5] P?SCHEL J,TUBOWITZ E.Inverse spectral theory academic press[M].New York:AMS,1987.
[6] DELRIO R,GRéBERT B.Inverse spectral result for AKNS systems with partial information on the potentials[J].Mathematical Physics,Analysis and Geometry,2001,4(3):229-244.
[7] MIKLóS H.On the inverse spectral theory of Schr?dinger and Dirac operators[J].Amer Math Soc Transl,2001,353:4155-4171.
[8] AMOUR L,RAOUX T.Inverse spectral results for Schr?dinger operators on the unit interval with potentials in Lp spaces[J].Inverse Problems,2007,23:2367-2373.
[9] LENIN,B Js.Distribution of zeros of entire functions[M].New York:AMS,1964.
[2] WATSON B A.Inverse spectral problems for weighted Dirac systems[J].Inverse Problem,1999,15(3):793-80.
[3] GASYMOV M G,LEVITAN B M.Determining the Dirac system from scattering phase[J].Dokl Akad Nauk SSSR,1996,167:1219-1222.
[4] LEVITAN B M,SARGSJAN I S.Sturm-Liouville and Dirac operators[M].Berlin:Spriger,1988.
[5] P?SCHEL J,TUBOWITZ E.Inverse spectral theory academic press[M].New York:AMS,1987.
[6] DELRIO R,GRéBERT B.Inverse spectral result for AKNS systems with partial information on the potentials[J].Mathematical Physics,Analysis and Geometry,2001,4(3):229-244.
[7] MIKLóS H.On the inverse spectral theory of Schr?dinger and Dirac operators[J].Amer Math Soc Transl,2001,353:4155-4171.
[8] AMOUR L,RAOUX T.Inverse spectral results for Schr?dinger operators on the unit interval with potentials in Lp spaces[J].Inverse Problems,2007,23:2367-2373.
[9] LENIN,B Js.Distribution of zeros of entire functions[M].New York:AMS,1964.