a1 Institut für Mathematik, RWTH Aachen
We consider the Friedrichs extension A of a minimal Sturm-Liouville operator L0 and show that A admits a Schrödinger factorization, i.e. that one can find first order differential operators Bk with where the μk are suitable numbers which optimally chosen are just the lower eigenvalues of A (if any exist). With the help of this theorem we derive for the special case L0u = −u″ + q(x)u with q(x) → 0 (|x| → ∞) the inequality
σd(A) being the discrete spectrum of A. This inequality is seen to be sharp to some extent.
(Received May 05 1977)