Fock 型空间上的 Schödinger 测不准关系

数学物理学报 ›› 2023, Vol. 43 ›› Issue (5): 1321-1332.

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Fock 型空间上的 Schödinger 测不准关系

李文鑫(),连攀^*(),梁玉霞()

天津师范大学数学科学学院天津 300387

收稿日期:2022-09-20 修回日期:2023-04-10 出版日期:2023-10-26 发布日期:2023-08-09
通讯作者: 连攀 E-mail:liwenxin1116@163.com;panlian@tjnu.edu.cn;liangyx1986@126.com
作者简介:李文鑫，Email: liwenxin1116@163.com;|梁玉霞，Email: liangyx1986@126.com
基金资助:
国家自然科学基金(12101451)

The Schödinger Uncertainty Relation in the Fock-Type Spaces

Li Wenxin(),Lian Pan^*(),Liang Yuxia()

School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387

Received:2022-09-20 Revised:2023-04-10 Online:2023-10-26 Published:2023-08-09
Contact: Pan Lian E-mail:liwenxin1116@163.com;panlian@tjnu.edu.cn;liangyx1986@126.com
Supported by:
NSFC(12101451)

摘要/Abstract

摘要：

该文建立了 Fock 型空间上单边加权移位算子的 Schödinger 测不准关系, 并给出了等号成立时的显式表达, 进而推广了文献 [4] 中建立的 Fock 空间上 Heisenberg 型测不准关系并克服了文献 [16] 中的困难. 该文进一步将结果推广到多个算子情形, 还得到了单边加权移位算子的一个非自伴形式的测不准不等式.

关键词: Fock 空间, 测不准原理, 单边加权移位算子, Segal-Bargmann 变换, 求导算子

Abstract:

In this paper, the Schödinger uncertainty relation for the unilateral weighted shift operators on Fock space is established, and the explicit expression when the equality attained is given, which further extends the Heisenberg uncertainty relation on Fock space established in [4] and overcomes the difficulty in [16]. In addition, we generalize the uncertainty relation to the multiple operators case. A new uncertainty inequality in the form of non-self adjoint operators is obtained as well.

Key words: Fock space, Uncertainty Principle, Unilateral weighted shift operator, Segal-Bargmann transform, Derivation operator

中图分类号:

O177.1

李文鑫,连攀,梁玉霞. Fock 型空间上的 Schödinger 测不准关系[J]. 数学物理学报, 2023, 43(5): 1321-1332.

Li Wenxin,Lian Pan,Liang Yuxia. The Schödinger Uncertainty Relation in the Fock-Type Spaces[J]. Acta mathematica scientia,Series A, 2023, 43(5): 1321-1332.

参考文献 17

[1]	Alpay D, Colombo F, Sabadini I, Salomon G. The Fock space in the slice hyperholomorphic setting//Bernstein S, Kahler U, Sabadini I, Sommen F. Hypercomplex Analysis: New Perspectives and Applications Trends in Mathematics. Cham: Birkhäuser, 2014: 43-59
[2]	Bargmann V. On a Hilbert space of analytic functions and an associated integral transform. Comm Pure Appl Math, 1961, 14: 187-214 doi: 10.1002/(ISSN)1097-0312
[3]	Chen B, Lian P. Uncertainty relations for multiple operators without covariances. J Physics A: Math Theory, 2022, 55(9): 095303 doi: 10.1088/1751-8121/ac4ce8
[4]	陈泳, 朱克和. Fock 空间上的测不准原理, 中国科学: 数学, 2015, 45(11): 1847-1854 doi: 10.1360/N012015-00057
	Chen Y, Zhu K H. Uncertainty principles for the Fock space. Sci Sin Math, 2015, 45(11): 1847-1854 doi: 10.1360/N012015-00057
[5]	Folland G B, Sitaram A. The uncertainty principle: A mathematical survey. J Fourier Anal Appl, 1997, 3: 207-238 doi: 10.1007/BF02649110
[6]	Gonoskov I. Closed-form solution of a general three-term recurrence relation. Adv Difference Equ, 2014, 2014(1): 1-12 doi: 10.1186/1687-1847-2014-1
[7]	Hai P V, Khoi L H. Complex symmetry of weighted composition operators on the Fock space. J Math Anal Appl, 2016, 433: 1757-1771 doi: 10.1016/j.jmaa.2015.08.069
[8]	胡璋剑, 吕小芬. Fock 空间及其相关算子. 中国科学: 数学, 2015, 45(11): 1759-1778 doi: 10.1360/N012015-00141
	Hu Z J, Lv X F. Fock spaces and relative operators. Sci Sin Math, 2015, 45(11): 1759-1778 doi: 10.1360/N012015-00141
[9]	Le T. Normal and isometric weighted composition operators on the Fock space. Bull Lond Math Soc, 2014, 46(4): 847-856 doi: 10.1112/blms/bdu046
[10]	Lian P, Liang Y. Weighted composition operator on quaternionic Fock space. Banach J Math Anal, 2021, 15(1): 1-20 doi: 10.1007/s43037-020-00085-8
[11]	Kechrimparis S, Weigert S. Geometry of uncertainty relations for linear combinations of position and momentum. J Physics A: Math Theory, 2017, 51(2): 025303 doi: 10.1088/1751-8121/aa9cfc
[12]	屈非非, 邓冠铁, 温志红. Fock 空间上一般线性算子的不确定原理. 北京师范大学学报, 2017, 53(2): 133-136
	Qu F F, Deng G T, Wen Z H. Uncertainty principles for the linear operators on Fock space. Journal of Beijing Normal University, 2017, 53(2): 133-136
[13]	Seip K, Youssfi E H. Hankel operators on Fock spaces and related Bergman kernel estimates. J Geom Anal, 2013, 23: 170-201 doi: 10.1007/s12220-011-9241-9
[14]	Shi J, Liu X, Zhang N. On uncertainty principles for linear canonical transform of complex signals via operator methods. Signal Image Video Process, 2014, 8(1): 85-93
[15]	Wang X, Cao G, Zhu K H. BMO and Hankel operators on Fock-type spaces. J Geom Anal, 2015, 25(3): 1650-1665 doi: 10.1007/s12220-014-9488-z
[16]	吴海桂, 梁玉霞. Fock 型空间上的广义不确定原理. 数学物理学报, 2020, 40A(6): 1409-1419
	Wu H G, Liang Y X. The generalized uncertainty principle on Fock-type space. Acta Math Sci, 2020, 40A(6): 1409-1419
[17]	Zhu K H. Analysis on Fock Spaces. New York: Springer-Verlag, 2012

Fock 型空间上的 Schödinger 测不准关系

The Schödinger Uncertainty Relation in the Fock-Type Spaces

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