Open AccessGeneralized quasi-regular representation and its applications for shearlet transforms
Author(s) -
Zahra Amiri,
Rajab Ali Kamyabi Gol
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2103963a
Subject(s) - shearlet , mathematics , semidirect product , algebra over a field , locally compact space , representation theory , representation (politics) , pure mathematics , invariant (physics) , group (periodic table) , computer science , chemistry , organic chemistry , artificial intelligence , politics , political science , wavelet , law , mathematical physics
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.