Quantum probabilistic approach to the Segal-Bargmann transform and infinitely divisible laws

Segal-Bargmann 变换和无限可分定律的量子概率方法

• 批准号: 23540131
• 负责人: ASAI Nobuhiro
• 金额: $ 2.75万
• 依托单位: Aichi University of Education
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540131/
• 关键词: 量子確率論; 直交多項式; シーガル・バーグマン変換; ブレンケ型母関数; ｑ類似; q直交多項式; Boas-Buck型母関数; q超幾何級数; Brenke-Chihara問題; ｑ変形直交多項式; ヤコビ・セゲーパラメータ; ｑ変形超幾何級数

From the point of multiplicative renormalization method, we examined the Brenke-Chihara problem, which is to determine all orthogonal polynomials associated with the Brenke type generating functions. As a result, all of the Jacobi-Szego parameters and q-hypergeometric series representations for all MRM-factors are obtained, explicitly. Our paper was published from IDAQP, an international mathematics journal. We have begun to consider if there would exist q-Fourier or q-Segal-Bargmann transforms and associated convolution products in a meaningful way from the quantum(algebraic) probabilistic view point.

从乘法重整化方法的角度，我们研究了Brenke-Chihara问题，即确定与Brenke型母函数相关的所有正交多项式。得到了所有MRM-因子的所有Jacobi-Szego参数和q-超几何级数表示。我们的论文发表在国际数学期刊IDAQP上。我们已经开始从量子(代数)概率的角度考虑是否存在有意义的q-傅立叶变换或q-西格尔-巴格曼变换和相关的卷积乘积。

项目成果

The Brenke type generating functions and orthogonal polynomials

Brenke 型生成函数和正交多项式

• 发表时间: 2011
• 作者: 久保泉;浅井暢宏;Atsumi Ohara;永幡幸生;Tadashi Hayashi and Jun Sekine;N. Asai
• 通讯作者: N. Asai

On the Brenke-Chihara's orthogonal polynomials and related topics

关于 Brenke-Chihara 的正交多项式及相关主题

• 发表时间: 2013
• 作者: N. Asai;I. Kubo;and H-H. Kuo;Nobuhiro Asai;浅井暢宏
• 通讯作者: 浅井暢宏

The Brenke-Chihara polynomials and q-convolutions

Brenke-Chihara 多项式和 q 卷积

• 发表时间: 2013
• 作者: Douglas Bridges;Hajime Ishihara and Maarten McKubre-Jordens;N. Asai;Hajime Ishihara;N. Asai
• 通讯作者: N. Asai

Orthogonal polynomials originated from the Boas-Buck type generating functions

正交多项式起源于 Boas-Buck 型生成函数

• 发表时间: 2012
• 作者: Takashi Kato;Jun Sekine;and Hiromitsu Yamamoto;Y. Nagahata;N. Asai
• 通讯作者: N. Asai

MRM triples associated with Brenke type generating functions

与 Brenke 型生成函数相关的 MRM 三元组

• 发表时间: 2012
• 作者: S. Kakihara;A. Ohara and T. Tsuchiya;Hajime Ishihara;Y. Nagahata;Y. Nagahata;N. Asai
• 通讯作者: N. Asai