Magnetic Pseudo-differential Operators with Hörmander Symbols Dominated by Tempered Weights

2025/11/10 by Thorn, Mikkel Hviid
Mathematics · Physics and Astronomy · #Mathematical Analysis and Transform Methods #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.2511.07184

Abstract

We extend the matrix representation of magnetic pseudo-differential operators in a tight Gabor frame from [arXiv:1804.05220, arXiv:2212.12229] to asymmetrical quantizations and smooth symbols dominated by a tempered weight (and not just decay/growth properties in the momentum variables). This leads to new results regarding the symbol calculus of such operators and their Schatten-class properties.

Citations

• Lieb-Robinson bounds in the continuum via localized frames
• A Proof of \mathfrakL²-Boundedness for Magnetic Pseudodifferential Super Operators via Matrix Representations With Respect to Parseval Frames
• Matrix representation of Magnetic pseudo-differential operators via tight Gabor frames
• A Schatten -von Neumann class criterion for the magnetic Weyl calculus
• Frames and operators in Schatten classes
• The magnetic formalism; new results

Related

• Matrix representation of Magnetic pseudo-differential operators via tight Gabor frames
• A Magnetic Pseudodifferential Calculus for Operator-Valued and Equivariant Operator-Valued Symbols
• The magnetic formalism; new results
• Peierls substitution and magnetic pseudo-differential calculus
• Spectral and Propagation Results for Magnetic Schroedinger Operators; a C*-Algebraic Framework