A spectral mapping theorem for perturbed Ornstein-Uhlenbeck operators on L^2(R^d)

TL;DR

This paper establishes a spectral mapping theorem for perturbed Ornstein-Uhlenbeck operators on L^2(R^d), using a perturbative resolvent construction and angular separation techniques.

Contribution

It introduces a novel spectral mapping theorem for perturbed Ornstein-Uhlenbeck operators under weak assumptions, expanding understanding of their spectral properties.

Findings

Proves a spectral mapping theorem for the semigroup generated by perturbed Ornstein-Uhlenbeck operators.

Develops a perturbative resolvent construction based on angular separation.

Utilizes the Gearhart-Prüss Theorem to establish spectral properties.

Abstract

We consider Ornstein-Uhlenbeck operators perturbed by a radial potential. Under weak assumptions we prove a spectral mapping theorem for the generated semigroup. The proof relies on a perturbative construction of the resolvent, based on angular separation, and the Gearhart-Pr\"u{\ss} Theorem.