Resolvent Estimates for Magnetic Schr\"odinger Operators and Their Applications to Related Evolution Equations
Resolvent Estimates for Magnetic Schr\"odinger Operators and Their Applications to Related Evolution Equations
复制标题
磁薛定格算子的求解估计及其在相关演化方程中的应用
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
K. Mochizuki
中科院分区：
文献类型：
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作者：
K. Mochizuki
本文综述了具有强奇异性的外势磁性薛定谔算子的一些基本结果。在适当的磁场和外部势的衰减条件下，讨论了以下主题：算子的自伴随性、广义特征函数的生长估计、极限吸收原理、均匀分解估计和相应演化方程的平滑性质。R v(x) = @1v1(x) + +@nvn(x)；r v (x) = (@jvk (x) @kvj (x)) 1 j k < n forr = (@1;; @n)和v (x) = (v1 (x);; vn (x))。我们还推导出b =r + b(x), b =rbr b, r =jxj, ~ x= x=r和@r = ~ xr。内积和
In this article we survey some basic results for the mag- netic Schrodinger operator with external potential which has a strong singularity. The following topics are treated under suitable decay con- ditions on the magnetic eld and external potential: Selfadjointness of the operator, Growth estimates of generalized eigenfunctions, Princi- ple of limiting absorption, Uniform resolvent estimates, and Smoothing properties for corresponding evolution equations. r v(x) = @1v1(x) + +@nvn(x); r v(x) = (@jvk(x) @kvj(x))1 j<k n forr = (@1; ;@n) and v(x) = (v1(x); ;vn(x)). We also putrb =r + ib(x), b =rbr b, r =jxj, ~ x = x=r and @r = ~ xr . The inner product and
DOI：
10.11429/sugaku1947.18.33
发表时间：
1966-06
期刊：
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影响因子：
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作者：
敏夫 加藤;晃生 池部
通讯作者：
敏夫 加藤;晃生 池部