Intrinsic ultracontractivity for Schrödinger semigroups based on cylindrical fractional Laplacian on the plane

2024/07/19 by Tadeusz Kulczycki, Kulczycki, Tadeusz, Kinga Sztonyk +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2407.14325

openalex publication_date 2024/07/19 · openalex created_date 2024/09/26 · openalex updated_date 2026/07/28

Abstract

We study Schrödinger operators on ℝ² H = (-(∂²)/(∂ x₁²))^α/2 + (-(∂²)/(∂ x₂²))^α/2 + V, for α∈ (0,2) and some sufficiently regular, radial, confining potentials V. We obtain necessary and sufficient conditions on intrinsic ultracontractivity for semigroups \e^-tH: t ≥ 0\. We also get sharp estimates of first eigenfunctions of H.

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