Optimal heat kernel estimates for schrödinger operators with magnetic fields in two dimensions
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Sharp smoothing estimates are proven for magnetic Schrödinger semigroups in two dimensions under the assumption that the magnetic field is bounded below by some positive constantB 0. As a consequence theL∞ norm of the associated integral kernel is bounded by theL∞ norm of the Mehler kernel of the Schrödinger semigroup with the constant magnetic fieldB 0.
KeywordsGaussian Function Heat Kernel Constant Magnetic Field Logarithmic Sobolev Inequality Heat Semigroup
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