Topic
Compactly generated group
About: Compactly generated group is a research topic. Over the lifetime, 25 publications have been published within this topic receiving 156 citations.
Papers
TL;DR: In this paper, a functional calculus on a total part of the weighted group algebra L PsyNet 1 PsyNet (G, ω) was developed and used to prove the Wiener property for a large class of weights.
Abstract: Let G be a compactly generated group of polynomial growth and ω a weight function on G. For a large class of weights we characterize symmetry of the weighted group algebra L
1
(G,ω). In particular, if the weight ω is sub-exponential, then the algebra L
1
(G,ω) is symmetric. For these weights we develop a functional calculus on a total part of L
1
(G,ω) and use it to prove the Wiener property.
42 citations
TL;DR: In this article, the authors consider the twisted Orlicz space and investigate its algebraic properties under the twisted convolution coming from the Young function and find sufficient conditions under which it becomes a Banach algebra.
Abstract: Let G be a locally compact group, let $\Omega:G\times G\to \mathbb{C}^*$ be a 2-cocycle, and let $\Phi$ be a Young function. In this paper, we consider the Orlicz space $L^\Phi(G)$ and investigate its algebraic property under the twisted convolution $\circledast$ coming from $\Omega$. We find sufficient conditions under which $(L^\Phi(G),\circledast)$ becomes a Banach algebra or a Banach $*$-algebra; we call it a {\it twisted Orlicz algebra}. Furthermore, we study its harmonic analysis properties, such as symmetry, existence of functional calculus, regularity, and having Wiener property, mostly for the case when $G$ is a compactly generated group of polynomial growth. We apply our methods to several important classes of polynomial as well as subexponential weights and demonstrate that our results could be applied to variety of cases.
18 citations
TL;DR: In this article, the authors give examples of such weighted Banach spaces and study some of their harmonic properties, such as symmetry, functional calculus, regularity, weak Wiener property, and existence of minimal ideals of a given hull.
Abstract: Let $G$ be a locally compact, compactly generated group of polynomial growth and let $\omega$ be a weight on $G$. Under proper assumptions on the weight $\omega$, the Banach space $L^p(G,\omega)$ is a Banach \ast-algebra. In this paper we give examples of such weighted $L^p$-algebras and we study some of their harmonic analysis properties, such as symmetry, existence of functional calculus, regularity, weak Wiener property, Wiener property, existence of minimal ideals of a given hull.
16 citations
TL;DR: In this paper, the authors give examples of such weighted L p -algebras and study some of their harmonic analysis properties, such as symmetry, functional calculus, regularity, weak Wiener property, and existence of minimal ideals of a given hull.
15 citations
TL;DR: In this article, the authors introduced the notion of locally compact topological spaces, which is an extension of the usage of the Geometry of Numbers, where G is the real-dimensional vector space R.
Abstract: 1. I n t r o d u c t i o n . Let G be a locally compact and (7-compact topological group and let H be a discrete subgroup of G. We shall use G/H to denote the space of right cosets Hx of H with the usual topology (cf. (8, pp. 26-28)) . Let /x be the left Haar measure in G. \\x induces a measure in the space G/Hf this measure will, wi thout ambiguity in this paper, also be denoted by fx. If JJL{G/H) is finite, the group H is called a lattice. If the space G/H is compact, then H is certainly a lattice and is called a bounded lattice. These terms are an extension of the usage of the Geometry of Numbers , where G is the real ^-dimensional vector space R. In this case any lattice is generated by n linearly independent vectors, all lattices are bounded, and the whole family of lattices is permuted transit ively by the automorphisms of G (which are the non-singular linear transformations). The constant n(G/H) is called the determinant of H in this case. T h e family of all lattices in Euclidean space forms a locally compact topological space. In (7) Mahler proved the following
15 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 1 |
| 2019 | 1 |
| 2018 | 1 |
| 2017 | 2 |
| 2016 | 1 |
| 2015 | 1 |