Trace Formulae for the Eigenfunctions of Periodic Finite-Bands Dirac Operator  

作　　者：Zhen LI Guangyao ZHANG Zhongyao WANG 

机构地区：[1]Department of Mathematics,Zhengzhou University [2]School of Science,Huzhou University

出　　处：《Journal of Mathematical Research with Applications》2015年第5期484-492,共9页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11326131);the Natural Science Foundation of Zhejiang Province(Grant No.LQ14A010009);the Natural Science Foundation of Huzhou City(Grant No.2013YZ06)

摘　　要：In this paper,we deal with a Dirac operator with periodic and finite-bands potentials.Taking advantage of the commutativity of the monodromy operator and the Dirac operator,we define the Bloch functions and multiplicator curve.Further,we obtain the formulae of Dubrovin-Novikov＇s type,which illustrate the inherent relations between the Bloch functions and potentials.Finally,we get the trace formulae of eigenfunctions corresponding to the left end-points,right end-points and all end-points of the spectral bands by calculation of residues on the complex sphere,respectively.In this paper,we deal with a Dirac operator with periodic and finite-bands potentials.Taking advantage of the commutativity of the monodromy operator and the Dirac operator,we define the Bloch functions and multiplicator curve.Further,we obtain the formulae of Dubrovin-Novikov＇s type,which illustrate the inherent relations between the Bloch functions and potentials.Finally,we get the trace formulae of eigenfunctions corresponding to the left end-points,right end-points and all end-points of the spectral bands by calculation of residues on the complex sphere,respectively.

关 键 词：Dirac bands Operator formulae Bloch inherent operators imaginary illustrate residues 

分 类 号：O174[理学—数学]