# On the extremal extensions of a non-negative Jacobi operator

## TL;DR

This paper characterizes all non-negative self-adjoint extensions of a minimal non-negative matrix-valued Jacobi operator using boundary triplets and Weyl functions, providing explicit parametrizations of these extensions.

## Contribution

It introduces a method to describe and parametrize all non-negative self-adjoint extensions of matrix-valued Jacobi operators via boundary triplets and Weyl functions.

## Key findings

- Explicit description of Friedrichs and Krein extensions.
- Parameterization of all non-negative self-adjoint extensions.
- Application of boundary triplet technique to matrix-valued operators.

## Abstract

We consider minimal non-negative Jacobi operator with $p\times p-$matrix entries. Using the technique of boundary triplets and the corresponding Weyl functions, we describe the Friedrichs and Krein extensions of the minimal Jacobi operator. Moreover, we parameterize the set of all non-negative self-adjoint extensions in terms of boundary conditions.