Spectral Shift Function in the Large Coupling Constant Limit

Abstract

In the large-coupling constant limit we obtain an asymptotic expansion in powers of \( \mu ^{{ - \frac{1} {\delta }}} \) of the derivative of the spectral shift function corresponding to \( {\left( { - \Delta + \mu W(x), - \Delta } \right)} \). Here the potential W(x) is positive and \( W(x) \sim \omega _{0} (\frac{x} {{|x|}})|x|^{{ - \delta }} \) near infinity for some δ> n and ω0 ∈C∞ (Sn-1).