Mathematics Colloquium

Heinz Langer

(Vienna University)

"Sturm-Liouville operators with singularities and indefinite inner products"

Date: Mon, November 28, 2011
Time: 17:15
Place: Research II Lecture Hall

Abstract: We consider the differential operator $-\dfrac{d^2y(x)}{dx^2}+ \dfrac{q_0}{(x-1)^2}$ on an interval $[0,a],\ a>1,\ q_0\ge 3/4$. Since $x=1$ is a limit point case from both sides, the classical $L^2$-space treatment within Weyl--Titchmarsh theory leads to the orthogonal sum of 2 differential operators on the intervals $[0,1)$ and $(1,a]$. This is, however, not always what is wanted. For certain examples it seems more natural to consider this operator in a space with an indefinite inner poduct. In the lecture we explain one such approach.