Complex Variables and Elliptic Equations, Volume (66), No (8), Year (2020-5) , Pages (1264-1286)

Title : ( Quaternionic inverse Fourier transforms on locally compact abelian groups )

Authors: Majid Jabbar Saadan Al Othman , Mohammad Janfada , Rajab Ali Kamyabi Gol ,

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In this paper, after introducing the concepts of quaternionic dual group and the quaternionic valued character on locally compact abelian group G2, the inverse of the quaternionic Fourier transform (QFT) on locally compact abelian groups is investigated. Due to the non-commutativity of multiplication of quaternions, there are different types of QFTs right, left and two-sided quaternionic Fourier transform. We focus on the right-sided quaternionic Fourier transform (RQFT) and two-sided quaternionic Fourier transform (SQFT). We establish the quaternionic Plancherel and inversion theorems for the square integrable quaternionic-valued signals on G2, the space L2 G2,H , where G is a locally compact abelian group. Also RQFT on the space L2 G2,H is studied. Furthermore relations between RQFT and SQFT are discussed. These results provide new proofs for the classical inverse Fourier transform, Plancherel theorem, etc. in L2(G).


, Locally compact abelian groups, quaternion inverse Fourier transforms, Plancherel’s theorem
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author = {Al Othman, Majid Jabbar Saadan and Janfada, Mohammad and Kamyabi Gol, Rajab Ali},
title = {Quaternionic inverse Fourier transforms on locally compact abelian groups},
journal = {Complex Variables and Elliptic Equations},
year = {2020},
volume = {66},
number = {8},
month = {May},
issn = {1747-6933},
pages = {1264--1286},
numpages = {22},
keywords = {Locally compact abelian groups; quaternion inverse Fourier transforms; Plancherel’s theorem},


%0 Journal Article
%T Quaternionic inverse Fourier transforms on locally compact abelian groups
%A Al Othman, Majid Jabbar Saadan
%A Janfada, Mohammad
%A Kamyabi Gol, Rajab Ali
%J Complex Variables and Elliptic Equations
%@ 1747-6933
%D 2020