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1.
Let be a second countable locally compact abelian group. The aim of this paper is to characterize the left translates on the Heisenberg group to be frames and Riesz bases in terms of the group Fourier transform. 相似文献
2.
Osamu Hatori 《Proceedings of the American Mathematical Society》1998,126(8):2351-2353
Every bounded regular Borel measure on noncompact LCA groups is a sum of an absolutely continuous measure and a measure with natural spectrum. The set of bounded regular Borel measures with natural spectrum on a nondiscrete LCA group whose Fourier-Stieltjes transforms vanish at infinity is closed under addition if and only if is compact.
3.
The well-known Skitovich-Darmois theorem asserts that a Gaussian distribution is characterized by the independence of two
linear forms of independent random variables. The similar result was proved by Heyde, where instead of the independence, the
symmetry of the conditional distribution of one linear form given another was considered. In this article we prove that the
Heyde theorem on a locally compact Abelian group X remains true if and only if X contains no elements of order two. We describe also all distributions on the two-dimensional torus which are characterized by the symmetry of the conditional distribution of one linear form given another. In so doing we
assume that the coefficients of the forms are topological automorphisms of X and the characteristic functions of the considering random variables do not vanish. 相似文献
4.
Average sampling is motivated by realistic needs, e.g., physical limitation of acquisition devices or characteristics of sampling procedure. As an extension of the average sampling, we study generalized average sampling in shift invariant spaces with frame generators, in which averages are taken from suitable channeled version of signals. Illustrative examples are given. 相似文献
5.
We develop an asymmetric multi-channel sampling on a shift invariant space V(?) with a Riesz generator ?(t) in L2(R), where each channeled signal is assigned a uniform but distinct sampling rate. We use Fourier duality between V(?) and L2[0,2π] to find conditions under which there is a stable asymmetric multi-channel sampling formula on V(?). 相似文献
6.
Mark Mandelkern 《Mathematical Logic Quarterly》1993,39(1):213-216
Although classically every open subspace of a locally compact space is also locally compact, constructively this is not generally true. This paper provides a locally compact remetrization for an open set in a compact metric space and constructs a one-point compactification. MSC: 54D45, 03F60, 03F65. 相似文献
7.
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
8.
Rodney Nillsen 《Monatshefte für Mathematik》1992,114(1):77-82
A special case of the main result proved in this paper is the following. IfG is a locally compact, -compact, non-compact connected abelian group, thenL
2
(G)={f–*f:fL
2
(G), L
1
(G), 0 and
G
=1}. In this case, any topologically invariant linear form onL
2
(G) is 0. 相似文献
9.
QIU ZhiJian School of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2008,51(1):131-142
Let G be a bounded open subset in the complex plane and let H~2(G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1-1 with respect to the Lebesgue measure on D and if the Riemann map belongs to the weak-star closure of the polynomials in H~∞(W). Our main theorem states: in order that for each M∈Lat (M_z), there exist u∈H~∞(G) such that M=∨{uH~2(G)}, it is necessary and sufficient that the following hold: (1) each component of G is a perfectly connected domain; (2) the harmonic measures of the components of G are mutually singular; (3) the set of polynomials is weak-star dense in H~∞(G). Moreover, if G satisfies these conditions, then every M∈Lat (M_z) is of the form uH~2(G), where u∈H~∞(G) and the restriction of u to each of the components of G is either an inner function or zero. 相似文献
10.
Reinhard DiestelPhilipp Sprüssel 《Topology and its Applications》2011,158(13):1626-1639
We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original graph-theoretical definition could be captured in the usual language for homology theories, so as to make it applicable to more general spaces. In this paper we provide such a general topological framework: we define a homology theory which satisfies the usual axioms, but which maintains the special role for ends that has made this homology work so well for graphs. 相似文献
11.
M. Filali 《Proceedings of the American Mathematical Society》1999,127(8):2325-2333
Let be a locally compact group, let be its group algebra, let be its usual measure algebra, let be the second dual of with an Arens product, and let be the conjugate of the space of bounded, left uniformly continuous, complex-valued functions on with an Arens-type product. We find all the finite-dimensional left ideals of these algebras. We deduce that such ideals exist in and if and only if is compact, and in (except those generated by right annihilators of ) and if and only if is amenable.
12.
M. Filali 《Proceedings of the American Mathematical Society》1999,127(6):1729-1734
Let be a discrete group, a commutative discrete cancellative semigroup or a locally compact abelian group. Let be the space of bounded, uniformly continuous, complex-valued functions on With an Arens-type product, the conjugate becomes a Banach algebra. We prove, that unlike left ideals, finite-dimensional right ideals exist in if and only if is compact.
13.
A pro-Lie group is a projective limit of a projective system of finite dimensional Lie groups. A prodiscrete group is a complete abelian topological group in which the open normal subgroups form a basis of the filter of identity neighborhoods. It is shown here that an abelian pro-Lie group is a product of (in general infinitely many) copies of the additive topological group of reals and of an abelian pro-Lie group of a special type; this last factor has a compact connected component, and a characteristic closed subgroup which is a union of all compact subgroups; the factor group modulo this subgroup is pro-discrete and free of nonsingleton compact subgroups. Accordingly, a connected abelian pro-Lie group is a product of a family of copies of the reals and a compact connected abelian group. A topological group is called compactly generated if it is algebraically generated by a compact subset, and a group is called almost connected if the factor group modulo its identity component is compact. It is further shown that a compactly generated abelian pro-Lie group has a characteristic almost connected locally compact subgroup which is a product of a finite number of copies of the reals and a compact abelian group such that the factor group modulo this characteristic subgroup is a compactly generated prodiscrete group without nontrivial compact subgroups.Mathematics Subject Classification (1991): 22B, 22E 相似文献
14.
15.
A. R. Mirotin 《Mathematische Nachrichten》2023,296(9):4108-4124
Necessary and sufficient conditions are given for the boundedness of Hausdorff operators on the generalized Hardy spaces , real Hardy space , , and for compact Abelian group G. Surprisingly, these conditions turned out to be the same for all groups and spaces under consideration. Applications to Dirichlet series are given. The case of the space of continuous functions on G and examples are also considered. 相似文献
16.
Jinjin Li 《Acta Mathematica Hungarica》2004,104(4):301-305
We continue to study the characterizations of paracompact locally compact spaces under certain quotient mappings, and discuss
the relationships among them, which expand the results on certain quotient images of paracompact locally compact spaces.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
17.
18.
Monatshefte für Mathematik - Let G be a locally compact abelian group. In this paper, we study derivations on the Banach algebra $$L_0^infty (G)^*$$ . We prove that any derivation on... 相似文献
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20.
Anthony To-ming Lau Peter F. Mah Ali Ü lger 《Proceedings of the American Mathematical Society》1997,125(7):2021-2027
In this paper we investigate when various Banach spaces associated to a locally compact group have the fixed point property for nonexpansive mappings or normal structure. We give sufficient conditions and some necessary conditions about for the Fourier and Fourier-Stieltjes algebras to have the fixed point property. We also show that if a -algebra has the fixed point property then for any normal element of , the spectrum is countable and that the group -algebra has weak normal structure if and only if is finite.