八元数偏移线性正则变换(octonion offset linear canonical transform,OOLCT)作为八元数线性正则变换(octonion linear canonical transform,OLCT)的推广形式,在高维非平稳信号时频调控中具有优势,但八元数非结合性使传统概率统计量定...八元数偏移线性正则变换(octonion offset linear canonical transform,OOLCT)作为八元数线性正则变换(octonion linear canonical transform,OLCT)的推广形式,在高维非平稳信号时频调控中具有优势,但八元数非结合性使传统概率统计量定义失效,且现有研究多聚焦四元数域,缺乏三维OOLCT(3D-OOLCT)域的严谨概率框架。本文将基础概率理论引入3D-OOLCT领域,构建兼容八元数特性的概率体系:首先,定义3D-OOLCT域中八元数值概率密度函数、分布函数、均值及特征函数;其次,证明特征函数定理;最后,通过算例推导验证特定概率密度函数在3D-OOLCT域的特征函数表达式。该研究填补OOLCT域与概率理论结合的空白,完善八元数变换理论,为三维高维随机信号统计分析提供新工具,也为后续相关工程应用奠定数理基础。展开更多
对各类展式的误差和函数的研究从21世纪初就开始了,研究人员不断深入探讨其各种性质,如连续性、周期性、有界性、介值性等,同时给出函数图像的Hausdorff维数。在本文中,我们将探讨Hurwitz连分数的误差和函数,提出一些相关的性质,并研究...对各类展式的误差和函数的研究从21世纪初就开始了,研究人员不断深入探讨其各种性质,如连续性、周期性、有界性、介值性等,同时给出函数图像的Hausdorff维数。在本文中,我们将探讨Hurwitz连分数的误差和函数,提出一些相关的性质,并研究其图像。The study of error-sum functions of expansions has been ongoing since the beginning of the 21st century, and researchers have been delving into various properties such as continuity, periodicity, boundedness, median, etc., along with giving the Hausdorff dimension of the graphs of the functions. In this paper, we will explore the error-sum function of Hurwitz continued fractions, present some related properties, and study their graphs.展开更多
LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional...LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.展开更多
文摘八元数偏移线性正则变换(octonion offset linear canonical transform,OOLCT)作为八元数线性正则变换(octonion linear canonical transform,OLCT)的推广形式,在高维非平稳信号时频调控中具有优势,但八元数非结合性使传统概率统计量定义失效,且现有研究多聚焦四元数域,缺乏三维OOLCT(3D-OOLCT)域的严谨概率框架。本文将基础概率理论引入3D-OOLCT领域,构建兼容八元数特性的概率体系:首先,定义3D-OOLCT域中八元数值概率密度函数、分布函数、均值及特征函数;其次,证明特征函数定理;最后,通过算例推导验证特定概率密度函数在3D-OOLCT域的特征函数表达式。该研究填补OOLCT域与概率理论结合的空白,完善八元数变换理论,为三维高维随机信号统计分析提供新工具,也为后续相关工程应用奠定数理基础。
文摘对各类展式的误差和函数的研究从21世纪初就开始了,研究人员不断深入探讨其各种性质,如连续性、周期性、有界性、介值性等,同时给出函数图像的Hausdorff维数。在本文中,我们将探讨Hurwitz连分数的误差和函数,提出一些相关的性质,并研究其图像。The study of error-sum functions of expansions has been ongoing since the beginning of the 21st century, and researchers have been delving into various properties such as continuity, periodicity, boundedness, median, etc., along with giving the Hausdorff dimension of the graphs of the functions. In this paper, we will explore the error-sum function of Hurwitz continued fractions, present some related properties, and study their graphs.
文摘LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.
