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

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>08/2002
<mark>Journal</mark>Communications in Mathematical Physics
Issue number1
Volume229
Number of pages19
Pages (from-to)121-139
<mark>State</mark>Published
<mark>Original language</mark>English

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