共查询到20条相似文献,搜索用时 15 毫秒
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A. Vourdas 《Journal of Fourier Analysis and Applications》2010,16(5):748-767
Harmonic analysis on ℤ(p
ℓ
) and the corresponding representation of the Heisenberg-Weyl group HW[ℤ(p
ℓ
),ℤ(p
ℓ
),ℤ(p
ℓ
)], is studied. It is shown that the HW[ℤ(p
ℓ
),ℤ(p
ℓ
),ℤ(p
ℓ
)] with a homomorphism between them, form an inverse system which has as inverse limit the profinite representation of the
Heisenberg-Weyl group
\mathfrak HW[\mathbbZp,\mathbbZp,\mathbbZp]\mathfrak {HW}[{\mathbb{Z}}_{p},{\mathbb{Z}}_{p},{\mathbb{Z}}_{p}]. Harmonic analysis on ℤ
p
is also studied. The corresponding representation of the Heisenberg-Weyl group HW[(ℚ
p
/ℤ
p
),ℤ
p
,(ℚ
p
/ℤ
p
)] is a totally disconnected and locally compact topological group. 相似文献
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O. Surmanidze 《Journal of Mathematical Sciences》2014,197(6):807-857
In this paper, we study linearly topological groups. We introduce the notion of a weakly linearly compact group, which generalizes the notion of a weakly separable group, and examine the main properties of such groups. For weakly linearly compact groups, we construct the character theory and present an algebraic characterization of some classes of such groups. Some well-known theorems for periodic Abelian groups are generalized for the case of linearly discrete, topological Abelian groups; for linearly compact and linearly discrete topological Abelian groups, we also construct the character theory and study some important properties of linearly discrete groups. For linearly discrete, topological Abelian groups, we analyze the splittability condition (Theorem 3.12) and present the characteristic condition of decomposability of a discrete group G into the direct sum of rank-1 groups. We also present an algebraic characterization of linearly compact groups. We introduce the notion of a weakly linearly compact, topological Abelian group, which generalizes the notion of a weakly separable Abelian group, and examine some properties of such groups. These groups are a generalization of fibrous Abelian groups introduced by Vilenkin. We give an algebraic characterization of divisible, weakly locally compact Abelian groups that do not contain nonzero elements of finite order (Proposition 7.9). For weakly locally compact Abelian groups, we construct universal groups. 相似文献
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Johan Kustermans 《Journal of Functional Analysis》2002,194(2):410-459
We introduce the construction of induced corepresentations in the setting of locally compact quantum groups and prove that the resulting induced corepresentations are unitary under some mild integrability condition. We also establish a quantum analogue of the classical bijective correspondence between quasi-invariant measures and certain measures on the larger locally compact group. 相似文献
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In this article, we present the abstract harmonic analysis aspects of the operator-valued continuous Gabor transform (CGT) on second countable, non-unimodular, and type I locally compact groups. We show that the operator-valued continuous Gabor transform CGT satisfies a Plancherel formula and an inversion formula. As an example, we study these results on the continuous affine group. 相似文献
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Nick Dungey 《Probability Theory and Related Fields》2007,137(3-4):429-442
Let G be a compactly generated, locally compact group, and let T be the operator of convolution with a probability measure μ on G. Our main results give sufficient conditions on μ for the operator T to be analytic in L
p
(G), 1 < p < ∞, where analyticity means that one has an estimate of form for all n = 1, 2, ... in L
p
operator norm. Counterexamples show that analyticity may not hold if some of the conditions are not satisfied. 相似文献
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朱月萍 《数学物理学报(A辑)》2000,20(Z1):616-624
该文给出了Vilenkin群上加权局部Hardy空间的定义,它的原子分解及对偶性质,并且研究了一类卷积算子在其上的有界性. 相似文献
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Kumi Yasuda 《Journal of Theoretical Probability》2000,13(3):635-657
Our aim in this paper is to characterize some classes of infinitely divisible distributions on locally compact abelian groups. Firstly infinitely divisible distributions with no idempotent factor on locally compact abelian groups are characterized by means of limit distributions of sums of independent random variables. We introduce semi-selfdecomposable distributions on topological fields, and in case of totally disconnected fields we give a limit theorem for them. We also give a characterization of semistable laws on p-adic field and show that semistable processes are constructed as scaling limits of sums of i.i.d. 相似文献
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Mathematical Notes - 相似文献
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S. S. Pandey 《Southeast Asian Bulletin of Mathematics》2003,26(4):611-624
In this paper, two theorems about the compactness of almost invariant operators on homogeneous Banach spaces of distributions (in the sense of Feichtinger [11]) defined on a locally compact abelian group are proved. Our theorems generalize the corresponding results of K. de Leeuw [3] and Tewari and Madan [18] for operators on homogeneous Banach spaces on the circle group and Segal algebras on a compact abelian groups, respectively.AMS Subject Classification 2000: 43A85, 47B07. 相似文献
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We investigate conditions under which a partial density on a locally compact abelian group can be extended to a density.
The results allow applications to the theory of uniform distribution of sequences in locally compact abelian groups.
Received August 27, 2001 Published online July 12, 2002 相似文献
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本文主要研究了Vilenkin群上的加权Hardy空间的原子分解,证明了一个加权H^p乘子定理并给出其应用。 相似文献
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Jan Hollevoet 《Mathematische Nachrichten》1995,176(1):93-110
A class of locally compact quantum semigroups in the sense of WORONOWICZ , containing the quantized Heisenberg group, is studied. The underlying quantum space is described in terms of a crossed product. We show the existence of a universal corepresentation and a Pontryagin dual, which turns out to be a twisted crossed product. The Pontryagin duality for these quantum semigroups is investigated. 相似文献
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Wojciech Jaworski 《Journal of Theoretical Probability》1997,10(4):967-989
Let G be a noncompact locally compact group. We show that a necessary and sufficient condition in order that G support an adapted probability measure whose concentration functions fail converge to zero is that G be the semidirect product
, where is an automorphism of N contractive modulo a compact subgroup. Any adapted a probability measure whose concentration functions fail to converge to zero has the form =v×1 where v is a probability measure on N. If G is unimodular then the concentration functions of an adapted probability measure fail to converge to zero if and only if is supported on a coset of a compact normal subgroup. 相似文献
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LetGbe a locally compact group. In this paper we study moduli of products of elements and of multipliers of Banach algebras which are related to locally compact groups and which admit lattice structure. As a consequence, we obtain a characterization of operators onL∞(G) which commute with convolutions whenGis amenable as discrete. 相似文献