A New Method Of Spectral Theory Of Anti-function Further Study

In this paper, we study the A-function introduced by Barry Simon in his new approach to inverse spectral theory. Firstly, we prove that the A-function and the potential are continuously dependent; secondly, we give the representation of A-function with Weyl function m; thirdly, we discuss the relationship between the A-function and the spectral measure, the spectrum; finally, we give a representation of Weyl function with the A-function on the upper and lower half complex plane by analytic continuation.