The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a l...In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a length 2t real GFT(a,b)(a = +/-1/2, b = +/-1/2) is 2(t+1) - 2. Practical algorithms which meet the lower bounds of multiplications are given.展开更多
Braverman and Kazhdan(2000)introduced influential conjectures aimed at generalizing the Fourier transform and the Poisson summation formula.Their conjectures should imply that quite general Langlands L-functions have ...Braverman and Kazhdan(2000)introduced influential conjectures aimed at generalizing the Fourier transform and the Poisson summation formula.Their conjectures should imply that quite general Langlands L-functions have meromorphic continuations and functional equations as predicted by Langlands'functoriality conjecture.As an evidence for their conjectures,Braverman and Kazhdan(2002)considered a setting related to the so-called doubling method in a later paper and proved the corresponding Poisson summation formula under restrictive assumptions on the functions involved.The connection between the two papers is made explicit in the work of Li(2018).In this paper,we consider a special case of the setting in Braverman and Kazhdan's later paper and prove a refined Poisson summation formula that eliminates the restrictive assumptions of that paper.Along the way we provide analytic control on the Schwartz space we construct;this analytic control was conjectured to hold(in a slightly different setting)in the work of Braverman and Kazhdan(2002).展开更多
In this paper we consider the Heckman-Opdam-Jacobi operatorΔ_(H J)on R^(d+1).We define the Heckman-Opdam-Jacobi intertwining operator V_(H J),which turns out to be the transmutation operator betweenΔ_(H J)and the La...In this paper we consider the Heckman-Opdam-Jacobi operatorΔ_(H J)on R^(d+1).We define the Heckman-Opdam-Jacobi intertwining operator V_(H J),which turns out to be the transmutation operator betweenΔ_(H J)and the LaplacianΔ_(d+1).Next we construct^(t)V_(H J)the dual of this intertwining operator.We exploit these operators to develop a new harmonic analysis corresponding toΔ_(H J).展开更多
文摘The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
文摘In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a length 2t real GFT(a,b)(a = +/-1/2, b = +/-1/2) is 2(t+1) - 2. Practical algorithms which meet the lower bounds of multiplications are given.
基金supported by the National Science Foundation of the USA(Grant Nos.DMS-1405708 and DMS-1901883)supported by the National Science Foundation of the USA(Grant Nos.DMS-1702218 and DMS-1848058)a start-up fund from the Department of Mathematics at Purdue University。
文摘Braverman and Kazhdan(2000)introduced influential conjectures aimed at generalizing the Fourier transform and the Poisson summation formula.Their conjectures should imply that quite general Langlands L-functions have meromorphic continuations and functional equations as predicted by Langlands'functoriality conjecture.As an evidence for their conjectures,Braverman and Kazhdan(2002)considered a setting related to the so-called doubling method in a later paper and proved the corresponding Poisson summation formula under restrictive assumptions on the functions involved.The connection between the two papers is made explicit in the work of Li(2018).In this paper,we consider a special case of the setting in Braverman and Kazhdan's later paper and prove a refined Poisson summation formula that eliminates the restrictive assumptions of that paper.Along the way we provide analytic control on the Schwartz space we construct;this analytic control was conjectured to hold(in a slightly different setting)in the work of Braverman and Kazhdan(2002).
文摘In this paper we consider the Heckman-Opdam-Jacobi operatorΔ_(H J)on R^(d+1).We define the Heckman-Opdam-Jacobi intertwining operator V_(H J),which turns out to be the transmutation operator betweenΔ_(H J)and the LaplacianΔ_(d+1).Next we construct^(t)V_(H J)the dual of this intertwining operator.We exploit these operators to develop a new harmonic analysis corresponding toΔ_(H J).
