On nuclear $L^p$-multipliers associated to the Harmonic oscillator

TL;DR

This paper investigates Hermite multipliers related to the harmonic oscillator, focusing on their nuclear properties, trace formulas, and spectral characteristics on Lebesgue spaces.

Contribution

It provides new insights into the nuclearity and trace formulas of harmonic oscillator multipliers, expanding understanding of their operator-theoretic properties.

Findings

Characterization of r-nuclear Hermite multipliers

Formulas for nuclear and spectral traces of these operators

Conditions for nuclearity on Lebesgue spaces

Abstract

In this paper we study multipliers associated to the harmonic oscillator (also called Hermite multipliers) belonging to the ideal of $r$-nuclear operators on Lebesgue spaces. We also study the nuclear trace and the spectral trace of these operators.