FOURIER TRANSFORM OF RANDOM VARIABLES ASSOCIATED WITH THE MULTI-DIMENSIONAL HEISENBERG LIE ALGEBRA

被引：2
|
作者：
Accardi, Luigi [1 ]
Boukas, Andreas [1 ]
机构：
[1] Univ Roma Tor Vergata, Ctr Vito Volterra, I-00133 Rome, Italy
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 143卷 / 09期
基金：
俄罗斯科学基金会;
关键词：
Bochner's theorem; vacuum characteristic function; Fock space; quantum random variable; multi-dimensional Heisenberg algebra;
D O I：
10.1090/proc/12539
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We compute the Fourier transform (or vacuum characteristic function) of quantum random variables (observables), defined as self-adjoint finite sums of Fock space operators, satisfying the multi-dimensional Heisenberg Lie algebra commutation relations. The main tool is a splitting formula for the multi-dimensional Heisenberg group obtained by Feinsilver and Pap.
引用
收藏
页码：4095 / 4101
页数：7
相关论文
共 50 条
  • [1] GEOMETRIC ALGEBRA ADAPTIVE FILTER BASED ON MULTI-DIMENSIONAL COMPLEX-VALUED RANDOM FOURIER FEATURES
    Zhang, Zihao
    Cai, Peng
    Shen, Minglin
    Huang, Gangyi
    Wang, Shiyuan
    2022 IEEE 32ND INTERNATIONAL WORKSHOP ON MACHINE LEARNING FOR SIGNAL PROCESSING (MLSP), 2022,
  • [2] An implementation of matched filtering using the multi-dimensional Fourier transform
    Mohanty, Soumya D.
    CLASSICAL AND QUANTUM GRAVITY, 2008, 25 (18)
  • [3] Acoustic direction finding using multi-dimensional Fourier transform
    Mazur, Jan
    2017 RADIOELECTRONIC SYSTEMS CONFERENCE, 2018, 10715
  • [4] Multi-dimensional graph fractional Fourier transform and its application
    School of Mathematics and Statistics, Beijing Institute of Technology, Beijing
    102488, China
    不详
    102488, China
    不详
    102488, China
    arXiv,
  • [5] Nonuniform Sampling in Lp-Subspaces Associated with the Multi-Dimensional Special Affine Fourier Transform
    Jiang, Yingchun
    Yang, Jing
    AXIOMS, 2024, 13 (05)
  • [6] The Heisenberg envelope for the Hochschild algebra of a finite-dimensional lie algebra
    Razmyslov Y.P.
    Pogudin G.A.
    Journal of Mathematical Sciences, 2013, 193 (4) : 580 - 585
  • [7] MULTI-DIMENSIONAL VIRASORO ALGEBRA
    LARSSON, TA
    PHYSICS LETTERS B, 1989, 231 (1-2) : 94 - 96
  • [8] Proposed Multi-Dimensional Algebra
    Hassoon, Kawthar Abdulabbas
    Yassein, Hassan Rashed
    INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2024, 19 (03): : 765 - 770
  • [9] Multi-dimensional quantum state sharing based on quantum Fourier transform
    Qin, Huawang
    Tso, Raylin
    Dai, Yuewei
    QUANTUM INFORMATION PROCESSING, 2018, 17 (03)
  • [10] Multi-dimensional quantum state sharing based on quantum Fourier transform
    Huawang Qin
    Raylin Tso
    Yuewei Dai
    Quantum Information Processing, 2018, 17
12345