Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - The local structure of the set of zero mode producing magnetic potentials.
AU - Elton, Daniel M.
N1 - RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
PY - 2002/8
Y1 - 2002/8
N2 - 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.
AB - 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.
U2 - 10.1007/s00220-002-0679-2
DO - 10.1007/s00220-002-0679-2
M3 - Journal article
VL - 229
SP - 121
EP - 139
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 1
ER -