The Spectral Shift Operator

1999/01/26 by Fritz Gesztesy, Gesztesy, Fritz, Konstantin A. Makarov +3
Mathematics · #FOS: Mathematics #Spectral Theory (math.SP) #math.SP

paper · pdf · doi:10.48550/arxiv.math/9901112

LaTeX, 28 pages

arxiv created 1999/01/26 · arxiv updated 2009/11/30

Abstract

We introduce the concept of a spectral shift operator and use it to derive Krein's spectral shift function for pairs of self-adjoint operators. Our principal tools are operator-valued Herglotz functions and their logarithms. Applications to Krein's trace formula and to the Birman-Solomyak spectral averaging formula are discussed.

Related

• Some Applications of the Spectral Shift Operator
• The Xi Operator and its Relation to Krein's Spectral Shift Function
• Spectral averaging for trace compatible operators
• The spectral shift function and the invariance principle
• Real-valued spectral shift functions for contractions and dissipative operators