SEMI-CLASSICAL RESOLVENT ESTIMATES FOR L ∞ POTENTIALS ON RIEMANNIAN MANIFOLDS
SEMI-CLASSICAL RESOLVENT ESTIMATES FOR L ∞ POTENTIALS ON RIEMANNIAN MANIFOLDS
复制标题
黎曼流形上 L ∞ 势的半经典解析估计
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
G. Vodev
中科院分区：
文献类型：
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作者：
G. Vodev
证明了具有实值L ∞位势的Schrodinger算子在具有紧致光滑边界的非紧连通黎曼流形上的半经典预解估计.我们证明了预解式的界依赖于无穷远处的man-ifold的结构。特别地，我们证明了对于紧支撑的实值L ∞位势和渐近欧氏流形，预解式界的形式为exp（Ch −4/3 log（h −1）），而对于渐近双曲流形，预解式界的形式为exp（Ch −4/3），其中C > 0是某个常数。
We prove semi-classical resolvent estimates for the Schrodinger operator with a real-valued L ∞ potential on non-compact, connected Riemannian manifolds which may have a compact smooth boundary. We show that the resolvent bound depends on the structure of the man-ifold at infinity. In particular, we show that for compactly supported real-valued L ∞ potentials and asymptoticaly Euclidean manifolds the resolvent bound is of the form exp(Ch −4/3 log(h −1)), while for asymptoticaly hyperbolic manifolds it is of the form exp(Ch −4/3), where C > 0 is some constant.
影响因子：
2.4
作者：
Datchev, Kiril;Shapiro, Jacob
通讯作者：
Shapiro, Jacob