In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequen...In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights.展开更多
带有限函数空间在数值分析、数据拟合等方面有广泛的应用,为许多问题提供了稳定性和可控性,能够有效地处理近似问题,找到最佳逼近方案。Paley-Wiener空间作为带有限函数空间的特殊情况,也是广泛应用于分析和信号处理等领域。本文研究加...带有限函数空间在数值分析、数据拟合等方面有广泛的应用,为许多问题提供了稳定性和可控性,能够有效地处理近似问题,找到最佳逼近方案。Paley-Wiener空间作为带有限函数空间的特殊情况,也是广泛应用于分析和信号处理等领域。本文研究加权多元Paley-Wiener空间在概率框架和平均框架下的逼近特征,特别地,利用离散化的方法估计了在概率框架和平均框架下,加权多元Paley-Wiener空间的线性n-宽度的精确渐进阶。Spaces of bounded functions have wide applications in numerical analysis, data fitting, and other fields. They provide stability and controllability for many problems, effectively handling approximation problems and finding optimal approximation solutions. As a special case of spaces of bounded functions, Paley-Wiener spaces are also widely used in fields such as analysis and signal processing. This paper studies the approximation properties of weighted multivariate Paley-Wiener spaces in probability and average settings. Specifically, by using discretization methods, it estimates the exact asymptotic order of the linear n-width of weighted multivariate Paley-Wiener spaces in both the probabilistic and average settings.展开更多
加权多元Paley-Wiener空间不仅在通讯、信息处理、数据压缩等方面有广泛应用,而且也是逼近定义在ℝ上的函数类的重要工具,因而得到广泛的深入研究。本文研究加权多元Paley-Wiener空间在概率框架和平均框架下的逼近特征,特别地,利用离散...加权多元Paley-Wiener空间不仅在通讯、信息处理、数据压缩等方面有广泛应用,而且也是逼近定义在ℝ上的函数类的重要工具,因而得到广泛的深入研究。本文研究加权多元Paley-Wiener空间在概率框架和平均框架下的逼近特征,特别地,利用离散化的方法估计了在概率框架和平均框架下,加权多元Paley-Wiener空间的Kolmogorov n-宽度的精确渐进阶。Weighted multivariate Paley-Wiener spaces have wide applications in communication, information processing, data compression, and other fields. They are also important tools for approximating classes of functions defined on ℝ, and thus have been extensively studied. This paper studies the approximation characteristics of weighted multivariate Paley-Wiener spaces in probability and average settings. In particular, by using discretization methods, the paper estimates the exact asymptotic order of the Kolmogorov n-width of weighted multivariate Paley-Wiener spaces in the probability and average settings.展开更多
This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourie...This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.展开更多
Associated with the Dirac operator and partial derivatives,this paper establishes some real PaleyWiener type theorems to characterize the Clifford-valued functions whose Clifford Fourier transform(CFT) has compact sup...Associated with the Dirac operator and partial derivatives,this paper establishes some real PaleyWiener type theorems to characterize the Clifford-valued functions whose Clifford Fourier transform(CFT) has compact support. Based on the Riemann-Lebesgue theorem for the CFT,the Boas theorem is provided to describe the CFT of Clifford-valued functions that vanish on a neighborhood of the origin.展开更多
In this paper, we obtain a characterization of the Paley-Wiener space with several variables, which is denoted by Bπ,p(Rn), 1≤p<∞, i.e., for 1<p<∞, Bπ,p(Rn) is isomorphic to lp(Zn), and for p=1, Bπ,1(Rn...In this paper, we obtain a characterization of the Paley-Wiener space with several variables, which is denoted by Bπ,p(Rn), 1≤p<∞, i.e., for 1<p<∞, Bπ,p(Rn) is isomorphic to lp(Zn), and for p=1, Bπ,1(Rn) is isomorphic to the discrete Hardy space with several variables, which is denoted by H(Zn).展开更多
The article considers the controllability of a diffusion equation with fractional integro-differential expressions.We prove that the resulting equation is nullcontrollable in arbitrary small time.Our method reduces es...The article considers the controllability of a diffusion equation with fractional integro-differential expressions.We prove that the resulting equation is nullcontrollable in arbitrary small time.Our method reduces essentially to the study of classical moment problems.展开更多
In this paper,we show that the elliptic cocenter of the Hecke algebra of a con-nected reductive p-adic group is contained in the rigid cocenter.As applications,we prove the trace Paley-Wiener theorem and the abstract ...In this paper,we show that the elliptic cocenter of the Hecke algebra of a con-nected reductive p-adic group is contained in the rigid cocenter.As applications,we prove the trace Paley-Wiener theorem and the abstract Selberg principle for mod-l representations.展开更多
基金Supported by the National Natural Science Foundation of China(12301101)the Guangdong Basic and Applied Basic Research Foundation(2022A1515110019 and 2020A1515110585)。
文摘In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights.
文摘带有限函数空间在数值分析、数据拟合等方面有广泛的应用,为许多问题提供了稳定性和可控性,能够有效地处理近似问题,找到最佳逼近方案。Paley-Wiener空间作为带有限函数空间的特殊情况,也是广泛应用于分析和信号处理等领域。本文研究加权多元Paley-Wiener空间在概率框架和平均框架下的逼近特征,特别地,利用离散化的方法估计了在概率框架和平均框架下,加权多元Paley-Wiener空间的线性n-宽度的精确渐进阶。Spaces of bounded functions have wide applications in numerical analysis, data fitting, and other fields. They provide stability and controllability for many problems, effectively handling approximation problems and finding optimal approximation solutions. As a special case of spaces of bounded functions, Paley-Wiener spaces are also widely used in fields such as analysis and signal processing. This paper studies the approximation properties of weighted multivariate Paley-Wiener spaces in probability and average settings. Specifically, by using discretization methods, it estimates the exact asymptotic order of the linear n-width of weighted multivariate Paley-Wiener spaces in both the probabilistic and average settings.
文摘加权多元Paley-Wiener空间不仅在通讯、信息处理、数据压缩等方面有广泛应用,而且也是逼近定义在ℝ上的函数类的重要工具,因而得到广泛的深入研究。本文研究加权多元Paley-Wiener空间在概率框架和平均框架下的逼近特征,特别地,利用离散化的方法估计了在概率框架和平均框架下,加权多元Paley-Wiener空间的Kolmogorov n-宽度的精确渐进阶。Weighted multivariate Paley-Wiener spaces have wide applications in communication, information processing, data compression, and other fields. They are also important tools for approximating classes of functions defined on ℝ, and thus have been extensively studied. This paper studies the approximation characteristics of weighted multivariate Paley-Wiener spaces in probability and average settings. In particular, by using discretization methods, the paper estimates the exact asymptotic order of the Kolmogorov n-width of weighted multivariate Paley-Wiener spaces in the probability and average settings.
基金supported by the Deanship of Scientific Research at King Khalid University,Saudi Arabia (R.G.P.1/207/43)。
文摘This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.
基金supported by National Natural Science Foundation of China(Grant No.11371007)
文摘Associated with the Dirac operator and partial derivatives,this paper establishes some real PaleyWiener type theorems to characterize the Clifford-valued functions whose Clifford Fourier transform(CFT) has compact support. Based on the Riemann-Lebesgue theorem for the CFT,the Boas theorem is provided to describe the CFT of Clifford-valued functions that vanish on a neighborhood of the origin.
基金the National Natural Science Foundation of China (19671012) Doctoral Programme institution of Higher Education Foundation
文摘In this paper, we obtain a characterization of the Paley-Wiener space with several variables, which is denoted by Bπ,p(Rn), 1≤p<∞, i.e., for 1<p<∞, Bπ,p(Rn) is isomorphic to lp(Zn), and for p=1, Bπ,1(Rn) is isomorphic to the discrete Hardy space with several variables, which is denoted by H(Zn).
基金Partially supported by the National Natural Science Foundation of China(10371011 and 10071005) and the Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry.
基金Supported by National Natural Science Foundation of China(No.11261024).
文摘The article considers the controllability of a diffusion equation with fractional integro-differential expressions.We prove that the resulting equation is nullcontrollable in arbitrary small time.Our method reduces essentially to the study of classical moment problems.
文摘In this paper,we show that the elliptic cocenter of the Hecke algebra of a con-nected reductive p-adic group is contained in the rigid cocenter.As applications,we prove the trace Paley-Wiener theorem and the abstract Selberg principle for mod-l representations.
