On Factorization of a Perturbation of a J-selfadjoint Operator Arising in Fluid Dynamics

TL;DR

This paper demonstrates that certain perturbations of J-selfadjoint second order differential operators, relevant in fluid dynamics, can be factorized, enabling analysis of their resolvent compactness and domain characterization.

Contribution

It introduces a factorization approach for perturbed J-selfadjoint operators, providing new tools for their spectral analysis in fluid dynamics contexts.

Findings

Proved factorization of specific perturbed J-selfadjoint operators.

Established compactness of the resolvent for these operators.

Determined the domain of the operators using the factorization.

Abstract

We prove that some perturbation of a J-selfadjoint second order differential operator admits factorization and use this new representation of the operator to prove compactness of its resolvent and to find its domain.