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The local structure of the set of zero mode producing magnetic potentials.

Research output: Contribution to journalJournal article

Published

Journal publication date08/2002
JournalCommunications in Mathematical Physics
Journal number1
Volume229
Number of pages19
Pages121-139
Original languageEnglish

Abstract

We consider the class of continuous magnetic potentials on ℝ3 which decay as o(|x|− 1). Within this class it is shown that the set of potentials whose associated Weyl-Dirac operator produces zero modes with multiplicity m forms a smooth submanifold of co-dimension m 2 when m= 0, 1, 2, and is contained in a smooth submanifold of co-dimension 2m− 1 when m≥ 3.

Bibliographic note

RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics