, Volume 14, Issue 5, pp 1413-1424

The Spectral Shift Function and the Friedel Sum Rule

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Abstract

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.

Communicated by Jan Derezinski.