scholarly journals Recent contributions to the embedding problem for probability measures on a locally compact group

1986 ◽  
Vol 19 (1) ◽  
pp. 119-131 ◽  
Author(s):  
H Heyer
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Probability Measures ◽  
Embedding Problem ◽  
Locally Compact

scholarly journals On a Certain Class of Semigroups of Operators

2011 ◽  
Vol 18 (02) ◽  
pp. 129-142 ◽  
Author(s):  
Paolo Aniello
Keyword(s):  
Banach Space ◽  
Compact Group ◽  
Banach Spaces ◽  
Locally Compact Group ◽  
Semigroups Of Operators ◽  
Probability Measures ◽  
Locally Compact ◽  
Quantum Dynamical ◽  
Interesting Class ◽  
Natural Way

We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced in the early 1970s by Kossakowski. Each randomly generated semigroup is associated, in a natural way, with a pair formed by a representation or an antirepresentation of a locally compact group in a Banach space and by a convolution semigroup of probability measures on this group. Examples of randomly generated semigroups having important applications in physics are briefly illustrated.

Contraction subgroups and semistable measures on p-adic Lie groups

1991 ◽  
Vol 110 (2) ◽  
pp. 299-306 ◽  
Author(s):  
S. G. Dani ◽  
Riddhi Shah
Keyword(s):  
Compact Group ◽  
Lie Groups ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Probability Measures ◽  
Compact Groups ◽  
Locally Compact ◽  
Significant Class

Continuous one-parameter semigroups {μt}t≥0 of probability measures on a locally compact group which are semistable with respect to some automorphism τ of the group, namely such that τ(μt) = μct for all t ≥ 0, for a fixed c ∈ (0, 1), have attracted considerable attention of various researchers in recent years (cf. [3], [5] and other references cited therein). A detailed study of semistable measures on (real) Lie groups is carried out in [5]. In this context it is of interest to study semistable measures on the class of p-adic Lie groups, which is another significant class of locally compact groups.

Collapsible probability measures and concentration functions on Lie groups

1997 ◽  
Vol 122 (1) ◽  
pp. 105-113 ◽  
Author(s):  
S. G. DANI ◽  
RIDDHI SHAH
Keyword(s):  
Probability Measure ◽  
Asymptotic Behaviour ◽  
Compact Group ◽  
Lie Groups ◽  
Locally Compact Group ◽  
Probability Measures ◽  
Locally Compact ◽  
Concentration Functions ◽  
Prove Theorem ◽  
Divergent Sequences

Given a locally compact group G and a probability measure μ on G it is of interest to know, in various situations, whether there exist divergent sequences {gn} such that {gn μg−1n is relatively compact (see for example [DM3] and [DS]); this phenomenon may be viewed as ‘collapsing’ of the measure. It is the purpose of this note to prove Theorem 1 below and give certain applications to the asymptotic behaviour of concentration functions.

scholarly journals Interpolation in wavelet spaces and the HRT-conjecture

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Eirik Berge
Keyword(s):  
Compact Group ◽  
Wavelet Transforms ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Space Structure ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Positive Type ◽  
Time Frequency ◽  
Hrt Conjecture

AbstractWe investigate the wavelet spaces $$\mathcal {W}_{g}(\mathcal {H}_{\pi })\subset L^{2}(G)$$ W g ( H π ) ⊂ L 2 ( G ) arising from square integrable representations $$\pi :G \rightarrow \mathcal {U}(\mathcal {H}_{\pi })$$ π : G → U ( H π ) of a locally compact group G. We show that the wavelet spaces are rigid in the sense that non-trivial intersection between them imposes strong restrictions. Moreover, we use this to derive consequences for wavelet transforms related to convexity and functions of positive type. Motivated by the reproducing kernel Hilbert space structure of wavelet spaces we examine an interpolation problem. In the setting of time–frequency analysis, this problem turns out to be equivalent to the HRT-conjecture. Finally, we consider the problem of whether all the wavelet spaces $$\mathcal {W}_{g}(\mathcal {H}_{\pi })$$ W g ( H π ) of a locally compact group G collectively exhaust the ambient space $$L^{2}(G)$$ L 2 ( G ) . We show that the answer is affirmative for compact groups, while negative for the reduced Heisenberg group.

The Superstability of the Generalized D'alembert Functional Equation

2003 ◽  
Vol 10 (3) ◽  
pp. 503-508 ◽  
Author(s):  
Elhoucien Elqorachi ◽  
Mohamed Akkouchi
Keyword(s):  
Functional Equation ◽  
Integral Equation ◽  
Compact Group ◽  
Locally Compact Group ◽  
Complex Numbers ◽  
Locally Compact

Abstract We generalize the well-known Baker's superstability result for the d'Alembert functional equation with values in the field of complex numbers to the case of the integral equation where 𝐺 is a locally compact group, μ is a generalized Gelfand measure and σ is a continuous involution of 𝐺.

scholarly journals Completely bounded bimodule maps and spectral synthesis

2017 ◽  
Vol 28 (10) ◽  
pp. 1750067 ◽  
Author(s):  
M. Alaghmandan ◽  
I. G. Todorov ◽  
L. Turowska
Keyword(s):  
Tensor Product ◽  
Compact Group ◽  
Closed Subset ◽  
Spectral Synthesis ◽  
Locally Compact Group ◽  
Product Formula ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Multiplication Algebra

We initiate the study of the completely bounded multipliers of the Haagerup tensor product [Formula: see text] of two copies of the Fourier algebra [Formula: see text] of a locally compact group [Formula: see text]. If [Formula: see text] is a closed subset of [Formula: see text] we let [Formula: see text] and show that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] then [Formula: see text] is a set of local spectral synthesis for [Formula: see text]. Conversely, we prove that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] and [Formula: see text] is a Moore group then [Formula: see text] is a set of spectral synthesis for [Formula: see text]. Using the natural identification of the space of all completely bounded weak* continuous [Formula: see text]-bimodule maps with the dual of [Formula: see text], we show that, in the case [Formula: see text] is weakly amenable, such a map leaves the multiplication algebra of [Formula: see text] invariant if and only if its support is contained in the antidiagonal of [Formula: see text].

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