SOME CONVERGENCE PROBLEMS REGARDING THE FRACTIONAL SCHRODINGER PROPAGATOR ON NONCOMPACT MANIFOLDS  

作　　者：潘亚丽 Yali PAN(School of Mathematics and Big Data,Chaohu University,Hefei 238024,China)

机构地区：[1]School of Mathematics and Big Data,Chaohu University,Hefei 238024,China

出　　处：《Acta Mathematica Scientia》2023年第5期2309-2319,共11页数学物理学报（B辑英文版）

基　　金：supported partly by the NationalNatural Science Foundation of China(12071437);the Natural Science Foundation from the Education Department of Anhui Province(KJ2020A0044);the Research Fund Project of Chaohu University(KYQD-2023016);the High Level Scientific Research Achievement Award Cultivation Project of Chaohu University(kj20zkjp04);the Key Construction Discipline of Chaohu University(kj22zdjsxk01)。

摘　　要：Let L be the Laplace-Beltrami operator.On an n-dimensional(n≥2),complete,noncompact Riemannian manifold M,we prove that if 0<α<1,s>α/2 and f∈Hs(M),then the fractional Schr?dinger propagator e(it|L|α/2)(f)(x)→f(x)a.e.as t→0.In addition,for when M is a Lie group,the rate of the convergence is also studied.These results are a non-trivial extension of results on Euclidean spaces and compact manifolds.

关 键 词：Schrodinger propagator noncompact manifolds SPECTRA 

分 类 号：O186.12[理学—数学]