F. Gesztesy, K. A. Makarov, and E. Tsekanovskii
An Addendum to Krein's Formula
(35K, LaTeX)
ABSTRACT. We provide additional results in connection with Krein's formula, which
describes the resolvent difference of two self-adjoint extensions $A_1$
and $A_2$ of a densely defined closed symmetric linear operator $\dot A$
with deficiency indices $(n,n),$ $n\in \bbN \cup \{ \infty \}$.~In
particular, we explicitly derive the linear fractional transformation
relating the
operator-valued Weyl-Titchmarsh $M$-functions $M_1(z)$ and $M_2(z)$
corresponding to $A_1$ and $A_2$.