Traces of Quantized Canonical Transformations Localized on a Finite Set of Points
Traces of Quantized Canonical Transformations Localized on a Finite Set of Points
复制标题
有限点集上的量化规范变换的踪迹
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
P. Sipailo
中科院分区：
文献类型：
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作者：
P. Sipailo
对于嵌入i：X ∈ M，M上的Fourier积分算子Φ定义为正则变换g：T*M {0} → T*M {0}的量子化，我们考虑子流形X上的算子i*Φi*，其中i* 和i* 是对应于嵌入i的边界和上边界算子.我们目前的条件下，这样的操作员的变换g的形式的傅立叶积分算子与纤维的余切丛在一个点。我们得到了一个显式公式计算该算子的振幅在局部坐标。
For an embedding i : X ↪ M of smooth manifolds and a Fourier integral operator Φ on M defined as the quantization of a canonical transformation g: T*M {0} → T*M {0}, we consider the operator i*Φi* on the submanifold X, where i* and i* are the boundary and coboundary operators corresponding to the embedding i. We present conditions on the transformation g under which such an operator has the form of a Fourier integral operator associated with the fiber of the cotangent bundle over a point. We obtain an explicit formula for calculating the amplitude of this operator in local coordinates.