Bernoulli噪声泛函上一类位势算子的谱性质

doi:10.6040/j.issn.1671-9352.0.2023.535

《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (12): 173-177.doi: 10.6040/j.issn.1671-9352.0.2023.535

Bernoulli噪声泛函上一类位势算子的谱性质

丁瑞鹤,王才士^*,张丽霞

西北师范大学数学与统计学院, 甘肃兰州 730070

发布日期:2025-12-10
通讯作者: 王才士(1962— ),男,教授,博士生导师,博士,研究方向为随机分析. E-mail:wangcs@nwnu.edu.cn
作者简介:丁瑞鹤(1993— ),女,硕士研究生,研究方向为数理统计学. E-mail:dingrhnwnu@163.com*通信作者:王才士(1962— ),男,教授,博士生导师,博士,研究方向为随机分析. E-mail:wangcs@nwnu.edu.cn
基金资助:
国家自然科学基金资助项目(1226108)

Spectral properties of some potential operators on Bernoulli noise functionals

DING Ruihe, WANG Caishi^*, ZHANG Lixia

School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Published:2025-12-10

摘要/Abstract

摘要： 考虑一类作用于Bernoulli噪声泛函的自伴算子N_u,此类算子可解释为某种位势算子。通过Full-Wiener积分变换,显式地求出一个与N_u酉等价的乘算子,由此进一步得到N_u的谱的显式表示;证明在适当条件下N_u仅有纯点谱。作为应用,考虑以N_u为Hamiltonian的量子系统,证明该系统是稳定的。

关键词: Bernoulli噪声泛函, 位势算子, 谱性质, 权函数

Abstract: This paper considers some self-adjoint operators N_u in Bernoulli noise functionals that essentially belong to the category of potential operators. By the Full-Wiener integral transform, the unitarily equivalent multiplication operators are explicitly obtained, and thus the explicit expressions of their spectrums are further obtained. Under some mild conditions, the fact that these operators have only pure point spectra is proved. Finally, in application, the proof that the quantum system with such an operator as the Hamiltonian is stable is proved.

Key words: Bernoulli noise functional, potential operator, spectral property, weight function

中图分类号:

O211.4

丁瑞鹤,王才士,张丽霞. Bernoulli噪声泛函上一类位势算子的谱性质[J]. 《山东大学学报(理学版)》, 2025, 60(12): 173-177.

DING Ruihe, WANG Caishi, ZHANG Lixia. Spectral properties of some potential operators on Bernoulli noise functionals[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(12): 173-177.

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Bernoulli噪声泛函上一类位势算子的谱性质

Spectral properties of some potential operators on Bernoulli noise functionals

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