The Research On One-dimensional Dirac Operator With Periodic Boundary Condition

The spectral problem of Dirac operator with periodic boundary conditions be discussed,note where p(x),r(x)∈C[0,π],λis complex parameter.First,the sameness problem of rank of eigenvalue and zero multiple numbers of entire func-tionω(λ) be considered;then,the trace formula of this problem is discussed,by a differential iden-tical relation and the residue method in function of complex variable;finally,the completeness of eigenfunction system and eigenfunction expansion theorem by the use of functional method be proofed.