Approximation of the Fractional Schr(o)dinger Propagator on Compact Manifolds

• 作者: Jie Cheng CHEN Da Shan FAN Fa You ZHAO
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（10）
• 页码范围: 1485-1496
• 页数: 12页
• 语种: 英文

摘要

Let L be a second order positive,elliptic differential operator that is self-adjoint with respect to some C∞ density dx on a compact connected manifold M.We proved that if 0 ＜ α ＜ 1,α/2 ＜ s ＜ α and f ∈ Hs(M) then the fractional Schr(o)dinger propagator eitLα/2 on M satisfies eitLα/2f(x)-f(x) =o(ts/α-ε) almost everywhere as t → 0+,for any ε ＞ 0.