Notes on (the Birmak-Krein-Vishik theory on) selfadjoint extensions of semibounded symmetric operators

TL;DR

This paper provides an explicit parametrization of all positive selfadjoint extensions of a densely defined, closed, positive operator, including identification of the Friedrichs extension, which is relevant for understanding operator extensions in functional analysis.

Contribution

It introduces a versatile parametrization method for positive selfadjoint extensions and explicitly identifies the Friedrichs extension within this framework.

Findings

Explicit parametrization of all positive selfadjoint extensions.

Identification of the Friedrichs extension via parameter specification.

Results remain relevant in current operator theory research.

Abstract

We give an explicit and versatile parametrization of all positive selfadjoint extensions of a densely defined, closed, positive operator. In addition, we identify the Friedrichs extension by specifying the parameter to which it corresponds. This is a manuscript that was circulated as the first part of the preprint "Two papers on selfadjoint extensions of symmetric semibounded operators", INCREST Preprint Series, July 1981, Bucharest, Romania, but never published. In this LaTeX typeset version, only typos and a few inappropriate formulations have been corrected, with respect to the original manuscript. I decided to post it on arXiv since, taking into account recent articles, the results are still of current interest. Tiberiu Constantinescu died in 2005.