On a Riesz Basis of Diagonally Generalized Subordinate Operator Matrices and Application to a Gribov Operator Matrix in Bargmann Space

TL;DR

This paper investigates the spectral properties and Riesz basis existence for certain unbounded operator matrices, with applications to Gribov operator matrices in Bargmann space, highlighting new spectral analysis techniques.

Contribution

It introduces new results on the spectrum and Riesz bases of diagonally and off-diagonally generalized subordinate operator matrices, with specific application to Gribov operators in Bargmann space.

Findings

Established conditions for the existence of Riesz bases

Analyzed spectral changes in operator matrices

Applied results to Gribov operator with Pomeron parameters

Abstract

In this paper, we study the change of spectrum and the existence of Riesz bases of specific classes of $n\times n$ unbounded operator matrices, called: diagonally and off-diagonally generalized subordinate block operator matrices. An application to a $n\times n$ Gribov operator matrix acting on a sum of Bargmann spaces, illustrates the abstract results. As example, we consider a particular Gribov operator matrix by taking special values of the real parameters of Pomeron.