Opuscula Math. 38, no. 5 (2018), 681-698

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.
  • Received: 2017-08-21.
  • Revised: 2017-12-15.
  • Accepted: 2017-12-20.
  • Published online: 2018-06-12.
Opuscula Mathematica - cover

Cite this article as:
Yaroslav I. Granovskyi, Leonid L. Oridoroga, Krein-von Neumann extension of an even order differential operator on a finite interval, Opuscula Math. 38, no. 5 (2018), 681-698, https://doi.org/10.7494/OpMath.2018.38.5.681

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