The Spectral Shift Function and The Friedel Sum Rule
  We study the relationship between the spectral shift function and the excess charge in potential scattering theory. Although these quantities are closely related to each other, they have been often formulated in different settings so far. Here we first give an alternative construction of the spectral shift function, and then we prove that the spectral shift function thus constructed yields the Friedel sum rule. 
Mahito Kohmoto, Tohru Koma, Shu Nakamura
math-ph cond-mat.other math.MP