TY - UNPB
T1 - Resolvent expansions of 3D magnetic Schrödinger operators and Pauli operators
AU - Jensen, Arne
AU - Kovarik, Hynek
PY - 2023
Y1 - 2023
N2 - We obtain asymptotic resolvent expansions at the threshold of the essential spectrum for magnetic Schrödinger and Pauli operators in dimension three. These operators are treated as perturbations of the Laplace operator in L2(R3) and L2(R3; C2), respectively. The main novelty of our approach is to show that the relative perturbations, which are first order differential operators, can be factorized in suitably chosen auxiliary spaces. This allows us to derive the desired asymptotic expansions of the resolvents around zero. We then calculate their leading and sub-leading terms explicitly. Analogous factorization schemes for more general perturbations, including e.g. finite rank perturbations, are discussed as well.
AB - We obtain asymptotic resolvent expansions at the threshold of the essential spectrum for magnetic Schrödinger and Pauli operators in dimension three. These operators are treated as perturbations of the Laplace operator in L2(R3) and L2(R3; C2), respectively. The main novelty of our approach is to show that the relative perturbations, which are first order differential operators, can be factorized in suitably chosen auxiliary spaces. This allows us to derive the desired asymptotic expansions of the resolvents around zero. We then calculate their leading and sub-leading terms explicitly. Analogous factorization schemes for more general perturbations, including e.g. finite rank perturbations, are discussed as well.
U2 - 10.48550/arXiv.2310.05874
DO - 10.48550/arXiv.2310.05874
M3 - Preprint
BT - Resolvent expansions of 3D magnetic Schrödinger operators and Pauli operators
PB - arXiv
ER -