Sharp semiclassical spectral asymptotics for local magnetic Schrödinger operators on Rd without full regularity

Soren Mikkelsen

doi:10.1007/s00023-024-01471-w

Sharp semiclassical spectral asymptotics for local magnetic Schrödinger operators on Rd without full regularity

Soren Mikkelsen

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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Abstract

We consider operators acting in L² (R^d) with d ≥3 that locally behave as a magnetic Schrödinger operator. For the magnetic Schrödinger operators, we suppose the magnetic potentials are smooth and the electric potential is five times differentiable and the fifth derivatives are Hölder continuous. Under these assumptions, we establish sharp spectral asymptotics for localised counting functions and Riesz means.

Original language	English
Pages (from-to)	1865-1906
Number of pages	42
Journal	Annales Henri Poincare
Volume	26
Issue number	5
Early online date	16 Jul 2024
DOIs	https://doi.org/10.1007/s00023-024-01471-w
Publication status	Published - 31 May 2025

Acknowledgements

The author is also grateful to the anonymous referees for carefully reading the manuscript and providing helpful remarks and comments that have helped improve the manuscript.

Funding

The author is grateful to the Leverhulme Trust for their support via Research Project Grant 2020-037.

Funders	Funder number
The Leverhulme Trust	2020-037

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10.1007/s00023-024-01471-wLicence: CC BY

Cite this

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abstract = "We consider operators acting in L2 (Rd) with d ≥3 that locally behave as a magnetic Schr{\"o}dinger operator. For the magnetic Schr{\"o}dinger operators, we suppose the magnetic potentials are smooth and the electric potential is five times differentiable and the fifth derivatives are H{\"o}lder continuous. Under these assumptions, we establish sharp spectral asymptotics for localised counting functions and Riesz means.",

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AB - We consider operators acting in L2 (Rd) with d ≥3 that locally behave as a magnetic Schrödinger operator. For the magnetic Schrödinger operators, we suppose the magnetic potentials are smooth and the electric potential is five times differentiable and the fifth derivatives are Hölder continuous. Under these assumptions, we establish sharp spectral asymptotics for localised counting functions and Riesz means.

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ER -

Sharp semiclassical spectral asymptotics for local magnetic Schrödinger operators on Rd without full regularity

Abstract

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