Intrinsic ultracontractivity for fractional Schrödinger operators

2018/08/10 by Beldi, Mohamed Ali
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1808.03269

Abstract

We establish sharp pointwise estimates for the ground states of some singular fractional Schrödinger operators on relatively compact Euclidean subsets. The considered operators are of the type (-Δ)^α/2|_Ω-V, where V∈ L¹_Loc and (-Δ)^α/2|_Ω is the fractional-Laplacian on an open subset Ω in ℝ^d with zero exterior condition . The intrinsic ultracontractivity property for such operators is discussed as well and a sharp large time asymptotic for their heat kernels is derived.

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