Krein-von Neumann extension of an even order differential operator on a finite interval

Abstract

We describe the Krein-von Neumann extension of minimal operator associated with the expression $\mathcal{A}:=(-1)^n\frac{d^{2n}}{dx^{2n}}$ on a finite interval $(a,b)$ in terms of boundary conditions. All non-negative extensions of the operator $A$ as well as extensions with a finite number of negative squares are described.