Resolvent estimates for the magnetic Hamiltonian with singular vector potentials and applications
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🧮 math.AP
math-phmath.MP
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resolventapplicationsestimateshamiltonianmagneticpotentialssingularvector
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For the magnetic Hamiltonian with singular vector potentials, we analytically continue the resolvent to a logarithmic neighborhood of the positive real axis and prove resolvent estimates there. As applications, we obtain asymptotic locations of resonances and a local smoothing estimate for solutions of the corresponding Schr\"odinger equation.
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