Holomorphic Hermite functions and ellipses
Holomorphic Hermite functions and ellipses
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全纯 Hermite 函数和椭圆
DOI：
10.1080/10652469.2017.1334057
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发表时间：
2017
影响因子：
1
通讯作者：
Hiroyuki Chihara
中科院分区：
文献类型：
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作者：
Hiroyuki Chihara
在1990年货车Eijndhoven和迈耶斯介绍了系统的全纯厄米函数和再生核希尔伯特空间与系统的复平面。此外，他们研究了家庭之间的关系，所有的希尔伯特空间和一类Gelfand-Shilov功能。之后，他们的系统的全纯厄米函数已被应用于研究量子化的复平面，组合学等，另一方面，作者最近介绍了系统的全纯厄米函数与椭圆在复平面上。本文证明了它们的全纯Hermite函数系是由椭圆的某些情形所决定的，而它们的再生核Hilbert空间是由Sjöstrand引入的Bargmann型变换所决定的Segal-Bargmann空间的某些情形.
In 1990 van Eijndhoven and Meyers introduced systems of holomorphic Hermite functions and reproducing kernel Hilbert spaces associated with the systems on the complex plane. Moreover they studied the relationship between the family of all their Hilbert spaces and a class of Gelfand–Shilov functions. After that, their systems of holomorphic Hermite functions have been applied to studying quantization on the complex plane, combinatorics, and etc. On the other hand, the author recently introduced systems of holomorphic Hermite functions associated with ellipses on the complex plane. The present paper shows that their systems of holomorphic Hermite functions are determined by some cases of ellipses, and that their reproducing kernel Hilbert spaces are some cases of the Segal–Bargmann spaces determined by the Bargmann-type transforms introduced by Sjöstrand.