Factorization of the Indefinite Convection-Diffusion Operator

TL;DR

This paper demonstrates the factorization of a non-self-adjoint indefinite convection-diffusion operator, enabling explicit domain construction and revealing its J-self-adjointness in a Krein space, advancing understanding of such operators.

Contribution

It introduces a novel factorization method for a class of non-self-adjoint operators and explicitly characterizes their domains and J-self-adjointness properties.

Findings

Operator admits factorization

Explicit domain construction achieved

Operator is J-self-adjoint in a Krein space

Abstract

We prove that some non-self-adjoint differential operator admits factorization and apply this new representation of the operator to construct explicitly its domain. We also show that this operator is J-self-adjoint in some Krein space.