Opuscula Math. 41, no. 6 (2021), 805-841

Opuscula Mathematica

The Krein-von Neumann extension of a regular even order quasi-differential operator

Minsung Cho
Seth Hoisington
Roger Nichols
Brian Udall

Abstract. We characterize by boundary conditions the Krein-von Neumann extension of a strictly positive minimal operator corresponding to a regular even order quasi-differential expression of Shin-Zettl type. The characterization is stated in terms of a specially chosen basis for the kernel of the maximal operator and employs a description of the Friedrichs extension due to Möller and Zettl.

Keywords: Krein-von Neumann extension, regular quasi-differential operator.

Mathematics Subject Classification: 47B25, 47E05, 34B24.

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  • Roger Nichols (corresponding author)
  • ORCID iD https://orcid.org/0000-0001-6583-4637
  • University of Tennessee at Chattanooga, Department of Mathematics (Dept. 6956), 615 McCallie Ave., Chattanooga, TN 37403, USA
  • Communicated by P.A. Cojuhari.
  • Received: 2021-09-10.
  • Revised: 2021-10-22.
  • Accepted: 2021-11-05.
  • Published online: 2021-11-29.
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Cite this article as:
Minsung Cho, Seth Hoisington, Roger Nichols, Brian Udall, The Krein-von Neumann extension of a regular even order quasi-differential operator, Opuscula Math. 41, no. 6 (2021), 805-841, https://doi.org/10.7494/OpMath.2021.41.6.805

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