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Spectral gap lower bound for the one-dimensional fractional Schrödinger operator in the interval
2012
Studia Mathematica
We prove the uniform lower bound for the difference λ_2 - λ_1 between first two eigenvalues of the fractional Schrödinger operator, which is related to the Feynman-Kac semigroup of the symmetric α-stable process killed upon leaving open interval (a,b) ∈ with symmetric differentiable single-well potential V in the interval (a,b), α∈ (1,2). "Uniform" means that the positive constant appearing in our estimate λ_2 - λ_1 ≥ C_α (b-a)^-α is independent of the potential V. In general case of α∈ (0,2),
doi:10.4064/sm209-3-5
fatcat:fdtogsrosbfc3dwyhyvwtqea7e