Separation of the Sturm–Liouville differential operator with an operator potential

摘要

In this paper we have studied the separation property of the Sturm–Liouville differential operator with operator potential of the form(1)Ay(x)=−ddxμ(x)dydx+V(x)y(x)in the space Hp(R), for p=1, 2, where μ(x)∈C1(R) is a positive continuous function on R and the potential V(x)∈L(λp) is a bounded linear operator on λp.