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 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.
