scholarly journals Generalized quasi-regular representation and its applications for shearlet transforms

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 963-972
Author(s):  
Z. Amiri ◽  
R.A. Kamyabi-Gol
Keyword(s):  
Representation Theory ◽  
Homogeneous Space ◽  
Linear Algebra ◽  
Radon Measure ◽  
Regular Representation ◽  
Higher Dimensions ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Algebra Approach

The construction of continuous shearlet transform has been extended to higher dimensions. It was generalized to a group that is topologically isomorphic to a group of semidirect product of locally compact groups. In this paper, by a unified theoretical linear algebra approach to the representation theory, a class of continuous shearlet transforms obtained from the generalized quasi-regular representation is presented. In order to develop such representation, we utilize a homogeneous space with a relatively invariant Radon measure as tool from computational and abstract harmonic analysis.

Contractive Representation Theory for the Unitary Group of C(X, M2)

1987 ◽  
Vol 39 (3) ◽  
pp. 612-624 ◽  
Author(s):  
Alan L. T. Paterson
Keyword(s):  
Representation Theory ◽  
Haar Measure ◽  
Unitary Group ◽  
Von Neumann Algebras ◽  
Unitary Representations ◽  
Theoretical Physics ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Von Neumann

One motivation for studying representation theory for the unitary group of a unital C*-algebra arises from Theoretical Physics. (In the latter connection, Segal [9] and Arveson [1] have developed a representation theory for G. Their approach is in a different direction from ours.) Another motivation for studying the representation theory of G arises out of the desire to unify the theories of amenable von Neumann algebras and amenable locally compact groups.A serious problem for such a representation theory is the absence of Haar measure on G in general.In [7], the author introduced the class RepdG of contractive unitary representations of G, the strong metric condition involved compensating for the lack of Haar measure.

ON CONSTRUCTION OF COHERENT STATES ASSOCIATED WITH SEMIDIRECT PRODUCTS

2008 ◽  
Vol 06 (05) ◽  
pp. 749-759 ◽  
Author(s):  
A. A. AREFIJAMAAL ◽  
R. A. KAMYABI-GOL
Keyword(s):  
Semidirect Product ◽  
Coherent States ◽  
Regular Representation ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Semidirect Products ◽  
Physics Literature ◽  
Semidirect Product Groups

Most of the interesting groups encountered in the physics literature are semidirect product groups. These groups are of the general form G = H ×τ K, where H and K are locally compact groups. In this paper, we consider the quasi regular representation on such a group G and investigate when it is possible to construct a family of coherent states associated to this representation.

On the Lp-conjecture for locally compact groups

2007 ◽  
Vol 89 (3) ◽  
pp. 237-242 ◽  
Author(s):  
F. Abtahi ◽  
R. Nasr-Isfahani ◽  
A. Rejali
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact

Ergodic actions of group extensions on von Neumann algebras

1989 ◽  
Vol 112 (1-2) ◽  
pp. 71-112
Author(s):  
Klaus Thomsen
Keyword(s):  
Fixed Point ◽  
Von Neumann Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Von Neumann ◽  
Finite Dimensional ◽  
Fixed Point Algebra ◽  
Atomic Centre

SynopsisWe consider automorphic actions on von Neumann algebras of a locally compact group E given as a topological extension 0 → A → E → G → 0, where A is compact abelian and second countable. Motivated by the wish to describe and classify ergodic actions of E when G is finite, we classify (up to conjugacy) first the ergodic actions of locally compact groups on finite-dimensional factors and then compact abelian actions with the property that the fixed-point algebra is of type I with atomic centre. We then handle the case of ergodic actions of E with the property that the action is already ergodic when restricted to A, and then, as a generalisation, the case of (not necessarily ergodic) actions of E with the property that the restriction to A is an action with abelian atomic fixed-point algebra. Both these cases are handled for general locally compact-countable G. Finally, we combine the obtained results to classify the ergodic actions of E when G is finite, provided that either the extension is central and Hom (G, T) = 0, or G is abelian and either cyclic or of an order not divisible by a square.

Locally compact groups with permutable closed subgroups

2021 ◽  
Vol 390 ◽  
pp. 107894
Author(s):  
Wolfgang Herfort ◽  
Karl H. Hofmann ◽  
Francesco G. Russo
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact
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