Opuscula Math. 38, no. 5 (2018), 681-698
https://doi.org/10.7494/OpMath.2018.38.5.681

Opuscula Mathematica

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

Yaroslav I. Granovskyi
Leonid L. Oridoroga

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.

Keywords: non-negative extension, Friedrichs' extension, Krein-von Neumann extension, boundary triple, Weyl function.

Mathematics Subject Classification: 47A05.

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• Yaroslav I. Granovskyi
• NAS of Ukraine, Institute of Applied Mathematics and Mechanics, Ukraine
• Leonid L. Oridoroga
• Donetsk National University, Donetsk, Ukraine
• Communicated by A.A. Shkalikov.
• Revised: 2017-12-15.
• Accepted: 2017-12-20.
• Published online: 2018-06-12.