Resolvent estimates for the magnetic Schrödinger operator in dimensions ≥2
Abstract
It is well known that the resolvent of the free Schrödinger operator on weighted L2 spaces has norm decaying like λ−12 at energy λ . There are several works proving analogous high frequency estimates for magnetic Schrödinger operators, with large long or short range potentials, in dimensions n≥3 . We prove that the same estimates remain valid in all dimensions n≥2 .
Main Authors
Format
Articles
Research article
Published
2020
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201908013739Use this for linking
Review status
Peer reviewed
ISSN
1139-1138
DOI
https://doi.org/10.1007/s13163-019-00316-z
Please see also
https://rdcu.be/bMF6b
Language
English
Published in
Revista Matemática Complutense
Citation
- Meroño, C. J., Potenciano-Machado, L., & Salo, M. (2020). Resolvent estimates for the magnetic Schrödinger operator in dimensions ≥2. Revista Matemática Complutense, 33(2), 619-641. https://doi.org/10.1007/s13163-019-00316-z
License
Funder(s)
European Commission
Research Council of Finland
Research Council of Finland
Funding program(s)
ERC Consolidator Grant
Centre of Excellence, AoF
Academy Project, AoF
ERC Consolidator Grant
Huippuyksikkörahoitus, SA
Akatemiahanke, SA
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Education and Culture Executive Agency (EACEA). Neither the European Union nor EACEA can be held responsible for them.
Additional information about funding
C.M. was supported by Spanish government predoctoral Grant BES-2015-074055 and projects MTM2014-57769-C3-1-P and MTM2017-85934-C3-3-P. L.P. and M.S. were supported by the Academy of Finland (Centre of Excellence in Inverse Modeling and Imaging, Grant Nos. 284715 and 309963) and by the European Research Council under Horizon 2020 (ERC CoG 770924)
Copyright© Universidad Complutense de Madrid 2019