Holomorphic Hermite Functions in Segal-Bargmann Spaces
Holomorphic Hermite Functions in Segal-Bargmann Spaces
复制标题
Segal-Bargmann 空间中的全纯 Hermite 函数
DOI：
10.1007/s11785-018-0804-7
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发表时间：
2019
影响因子：
0.8
通讯作者：
Hiroyuki Chihara
中科院分区：
文献类型：
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作者：
Mitsunori Nara;Hiroyuki Chihara
研究了Segal-Bargmann空间中的全纯Hermite函数系，Segal-Bargmann空间是复欧氏空间上整函数的Hilbert空间，由真实的欧氏空间上的Bargmann型积分变换确定.我们证明了对于任何严格小于与变换相关联的正Hermite矩阵的最小特征值的正参数，都可以找到一个全纯Hermite函数的生成元，该生成元的湮灭算子和生成算子满足正则对易关系.换句话说，我们找到了一些整函数可以是这样的生成元的充分必要条件。此外，我们还研究了完全正交性、特征值问题和Rodrigues公式。
We study systems of holomorphic Hermite functions in the Segal–Bargmann spaces, which are Hilbert spaces of entire functions on the complex Euclidean space, and are determined by the Bargmann-type integral transform on the real Euclidean space. We prove that for any positive parameter which is strictly smaller than the minimum eigenvalue of the positive Hermitian matrix associated with the transform, one can find a generator of holomorphic Hermite functions whose annihilation and creation operators satisfy canonical commutation relations. In other words, we find the necessary and sufficient conditions so that some kinds of entire functions can be such generators. Moreover, we also study the complete orthogonality, the eigenvalue problems and the Rodrigues formulas.