共查询到20条相似文献,搜索用时 15 毫秒
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We study the image of the theta correspondence from
to a rank one orthogonal group (over a number field). The image consists of cusp forms, the Fourier coefficients of which
satisfy a certain invariance property. We show that this property characterizes the image. The proof requires first an analogous
local statement (almost everywhere) and then a use of certain Rankin-Selberg integrals.
Partially supported by the Bat-Sheva de Rothschild Fund for the Advancement of Science and Technolog. 相似文献
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Kenneth D. Johnson 《Journal of Functional Analysis》1979,34(1):54-71
Let G be a linear semisimple Lie group of split rank one with K a maximal compact subgroup. In this paper, we consider the space Cc∞(G:F) of all functions in Cc∞(G) whose left and right K-translates span a finite-dimensional space. Using the analytic continuation of the principal series to define the Fourier transform, we give a characterization of the Fourier transform of the space Cc∞(G:F). This gives an analog of the classical Paley-Wiener theorem which gives a characterization of the Fourier transform of the space Cc∞(Rn). 相似文献
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Alexander Lubotzky 《Geometric And Functional Analysis》1991,1(4):405-431
We prove that if
is theK-rational points of aK-rank one semisimple group
over a non archimedean local fieldK, thenG has cocompact non-arithmetic lattices and if char(K)>0 also non-uniform ones. We also give a general structure theorem for lattices inG, from which we confirm Serre's conjecture that such arithmetic lattices do not satisfy the congruence subgroup property.Partially supported by a grant from the Bi-national Science Foundation U.S.-Israel. 相似文献
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Daniel Allcock 《Journal of Algebra》2009,321(9):2540-2544
One can develop the basic structure theory of linear algebraic groups (the root system, Bruhat decomposition, etc.) in a way that bypasses several major steps of the standard development, including the self-normalizing property of Borel subgroups. 相似文献
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GenKai Zhang 《中国科学 数学(英文版)》2017,60(11):2337-2348
We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n. 相似文献
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Roberto J. Miatello 《manuscripta mathematica》1979,29(2-4):249-276
In this paper we find a very explicit, simple form for the Plancherel measure for rank one, linear simple groups, including the normalizing constant. 相似文献
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《Mathematische Nachrichten》2017,290(13):2024-2051
We prove a genuine analogue of the Wiener Tauberian theorem for , where G is a real rank one noncompact, connected, semisimple Lie group with finite centre. This generalizes the corresponding result on the automorphism group of the unit disk by Y. Ben Natan, Y. Benyamini, H. Hedenmalm, and Y. Weit. We extend this result for hypergeometric transforms and as an application we prove an analogue of Furstenberg theorem on harmonic functions for hypergeometric transforms. 相似文献
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We consider the spherical complementary series of rank one Lie groups \(H_n={ SO }_0(n, 1; {\mathbb {F}})\) for \({\mathbb {F}}={\mathbb {R}}, {\mathbb {C}}, {\mathbb {H}}\). We prove that there exist finitely many discrete components in its restriction under the subgroup \(H_{n-1}={ SO }_0(n-1, 1; {\mathbb {F}})\). This is proved by imbedding the complementary series into analytic continuation of holomorphic discrete series of \(G_n=SU(n, 1)\), \(SU(n, 1)\times SU(n, 1)\) and SU(2n, 2) and by the branching of holomorphic representations under the corresponding subgroup \(G_{n-1}\). 相似文献
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Andrea Lucchini 《Archiv der Mathematik》1999,73(4):241-248
For any fixed k 3 7k \geq 7 there exist integers nk and ak such that if the ring R is generated by a set of m elements t1,...,tm, where 2t1-t122t_1-t_1^2 is a unit of finite multiplicative order, and n 3 nk+makn \geq n_k+ma_k, then the group En(R) generated by elementary transvections is an epimorphic image of the triangle group D(2,3,k).\Delta (2,3,k). 相似文献
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Richard Kueng Holger Rauhut Ulrich Terstiege 《Applied and Computational Harmonic Analysis》2017,42(1):88-116
We study the recovery of Hermitian low rank matrices from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form for some measurement vectors , i.e., the measurements are given by . The case where the matrix to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements ) via the PhaseLift approach, which has been introduced recently. We derive bounds for the number m of measurements that guarantee successful uniform recovery of Hermitian rank r matrices, either for the vectors , , being chosen independently at random according to a standard Gaussian distribution, or being sampled independently from an (approximate) complex projective t-design with . In the Gaussian case, we require measurements, while in the case of 4-designs we need . Our results are uniform in the sense that one random choice of the measurement vectors guarantees recovery of all rank r-matrices simultaneously with high probability. Moreover, we prove robustness of recovery under perturbation of the measurements by noise. The result for approximate 4-designs generalizes and improves a recent bound on phase retrieval due to Gross, Krahmer and Kueng. In addition, it has applications in quantum state tomography. Our proofs employ the so-called bowling scheme which is based on recent ideas by Mendelson and Koltchinskii. 相似文献
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A group G has finite rank r if every finitely generated subgroup of G is at most r-generator. If C is a class of groups then we let C* denote the class of groups G in which every proper subgroup of G is either of finite rank or in C. We let denote the class of soluble groups and the class of soluble groups of derived length at most d, where d is a positive integer. We let λ denote the set of closure operations
and let denote the λ-closure of the class of periodic locally graded groups. Amongst other results we prove that a soluble -group is either of finite rank or of derived length at most d and also that a group in the class is either locally soluble, or has finite rank, or is isomorphic to one of or for suitable locally finite fields .
The second author would like to thank the Department of Mathematics at Bucknell University for its hospitality while part
of this work was being done. 相似文献