Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds
Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds
复制标题
正格格和二维流形上低维微分算子和差分算子的离散谱对称性
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
I. Dynnikov
中科院分区：
文献类型：
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作者：
Сергей Петрович Новиков;S. Novikov;Иван Алексеевич Дынников;I. Dynnikov
内容? 1。简介：历史问题，一维Schr？丁格算子？非平稳的一维Schr？丁格方程？一维差分算子？拉普拉斯变换和二维薛尔？磁场中的定谔算子？差分方程和拉普拉斯变换。双曲的情况？正则格上椭圆型二维差分算子的拉普拉斯变换。三角形的方程，曲率？正四面体多维格上的因式分解和拉普拉斯变换。二维曲面上算子的因式分解和拉普拉斯变换。单纯的连接。归纳参考书目
Contents ?1. Introduction: history of the problem, the one-dimensional Schr?dinger operator ?2. The non-stationary one-dimensional Schr?dinger equation ?3. One-dimensional difference operators ?4. The Laplace transformation and the two-dimensional Schr?dinger operator in a magnetic field ?5. Difference equations and Laplace transformations. The hyperbolic case ?6. The Laplace transformation for elliptic two-dimensional difference operators on a regular lattice. Equations of a triangle, curvature ?7. Factorizations and Laplace transformations on many-dimensional lattices of regular tetahedra in ?8. Factorizations of operators and Laplace transformations on two-dimensional surfaces ?9. Simplicial connections. Generalizations Bibliography