Time-dependent Schrödinger perturbations of transition densities ∗

  title={Time-dependent Schr{\"o}dinger perturbations of transition densities ∗},
  author={Krzysztof Bogdan and Wolfhard Hansen and Tomasz Jakubowski},
We construct the fundamental solution of ∂t + ∆x + q(t, x), for functions q with a certain integral space-time relative smallness, in particular for those satisfying a relative negligibility. The resulting transition density is comparable to the Gaussian kernel in finite time, and it is even asymptotically equal to the Gaussian kernel (in small time) under the assumption of relative negligibility. The result is generalized to arbitrary strictly positive and finite time-inhomogeneous transition… CONTINUE READING

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