The Krein-von Neumann extension revisited
Functional Analysis
2022-10-11 v2 Spectral Theory
Abstract
We revisit the Krein-von Neumann extension in the case where the underlying symmetric operator is strictly positive and apply this to derive the explicit form of the Krein-von Neumann extension for singular, general (i.e., three-coefficient) Sturm-Liouville operators on arbitrary intervals. In particular, the boundary conditions for the Krein-von Neumann extension of the strictly positive minimal Sturm-Liouville operator are explicitly expressed in terms of generalized boundary values adapted to the (possible) singularity structure of the coefficients near an interval endpoint.
Keywords
Cite
@article{arxiv.2102.00685,
title = {The Krein-von Neumann extension revisited},
author = {Guglielmo Fucci and Fritz Gesztesy and Klaus Kirsten and Lance L. Littlejohn and Roger Nichols and Jonathan Stanfill},
journal= {arXiv preprint arXiv:2102.00685},
year = {2022}
}
Comments
26 pages. arXiv admin note: text overlap with arXiv:1910.13117