By employing the asymptotic behavior of the heat kernel of the nonlocal operator i(-Δ)α/2 and the theory of boundary values of analytic semigroups, we obtain a necessary and sufficient condition for the fractional Schrödinger semigroup to be strongly continuous. Our result extends Hörmander's one corresponding to the case of α=2 to the case ofα>2.
Our research results were published in "Archiv der Mathematik" under the title of "Boundary values of analytic semigroups generated by fractional Laplacians"(https://doi.org/10.1007/s00013-024-02004-x).
