On Selfadjoint Subspace of One-Speed Boltzmann Operator

TL;DR

This paper characterizes the selfadjoint subspace of the one-speed Boltzmann operator, showing it is nontrivial under specific polynomial and lattice conditions, with implications for transport operators.

Contribution

It provides a new description of the selfadjoint subspace for the Boltzmann operator and extends results to 3D transport operators.

Findings

Selfadjoint subspace is nontrivial if collision integral is polynomial and coefficient has lattice gaps.

Results apply to both one-speed Boltzmann and 3D transport operators.

Highlights conditions for nonselfadjointness in kinetic operators.

Abstract

The aim of the paper is to obtain a description of the selfadjoint subspace of the one-speed Boltzmann operator. It is proved that this subspace is nontrivial if the collision integral is polynomial and the multiplication coefficient has a lattice of gaps. A similar result is shown to hold for the 3-dimensional transport operator. Keywords: completely nonselfadjoint, Boltzmann operator, uncertainly principle.