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G. D. Dimov 《Acta Mathematica Hungarica》2010,129(4):314-349
Generalizing de Vries’ duality theorem [9], we prove that the category HLC of locally compact Hausdorff spaces and continuous maps is dual to the category DHLC of complete local contact algebras and appropriate morphisms between them. 相似文献
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Research partially supported by the Fundació Caixa Castelló (MI.25.043/92). 相似文献
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The Fourier coefficients of a smooth K-invariant function on a compact symmetric space M=U/K are given by integration of the function against the spherical functions. For functions with support in a neighborhood of the origin, we describe the size of the support by means of the exponential type of a holomorphic extension of the Fourier coefficients. 相似文献
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Martin E Walter 《Journal of Functional Analysis》1974,17(2):131-160
We make precise the following statements: B(G), the Fourier-Stieltjes algebra of locally compact group G, is a dual of G and vice versa. Similarly, A(G), the Fourier algebra of G, is a dual of G and vice versa. We define an abstract Fourier (respectively, Fourier-Stieltjes) algebra; we define the dual group of such a Fourier (respectively, Fourier-Stieltjes) algebra; and we prove the analog of the Pontriagin duality theorem in this context. The key idea in the proof is the characterization of translations of B(G) as precisely those isometric automorphisms Φ of B(G) which satisfy ∥ p ? eiθΦp ∥2 + ∥ p + eiθΦp ∥2 = 4 for all θ ∈ and all pure positive definite functions p with norm one. One particularly interesting technical result appears, namely, given x1, x2?G, neither of which is the identity e of G, then there exists a continuous, irreducible unitary representation π of G (which may be chosen from the reduced dual of G) such that π(x1) ≠ π(e) and π(x2) ≠ π(e). We also note that the group of isometric automorphisms of B(G) (or A(G)) contains as a (“large”) .closed, normal subgroup the topological version of Burnside's “holomorph of G.” 相似文献
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G.M. Feldman 《Journal of Functional Analysis》2010,258(12):3977-3987
We prove a group analogue of the well-known Heyde theorem where a Gaussian measure is characterized by the symmetry of the conditional distribution of one linear form given another. Let X be a locally compact second countable Abelian group containing no subgroup topologically isomorphic to the circle group T, G be the subgroup of X generated by all elements of order 2, and Aut(X) be the set of all topological automorphisms of X. Let αj,βj∈Aut(X), j=1,2,…,n, n?2, such that for all i≠j. Let ξj be independent random variables with values in X and distributions μj with non-vanishing characteristic functions. If the conditional distribution of L2=β1ξ1+?+βnξn given L1=α1ξ1+?+αnξn is symmetric, then each μj=γj∗ρj, where γj are Gaussian measures, and ρj are distributions supported in G. 相似文献
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A modular symbol is the fundamental class of a totally geodesic submanifold embedded in a locally Riemannian symmetric space , which is defined by a subsymmetric space . In this paper, we consider the modular symbol defined by a semisimple symmetric pair (G,G'), and prove a vanishing theorem with respect to the -component in the Matsushima-Murakami formula based on the discretely decomposable theorem of the restriction . In particular, we determine explicitly the middle Hodge components of certain totally real modular symbols on the locally
Hermitian symmetric spaces of type IV.
Received: December 8, 1996 相似文献