IJPAM: Volume 93, No. 5 (2014)
NON COMMUTATIVE FOURIER TRANSFORM AND
PLANCHEREL THEOREM FOR THE AFFINE GROUP
PLANCHEREL THEOREM FOR THE AFFINE GROUP
Kahar El-Hussein
, Badahi Ould Mohamed
Department of Mathematics
Faculty of Science
Al Furat University
Dear El Zore, SYRIA
Department of Mathematics
Faculty of Arts Science at Al Qurayat
Al-Jouf University, KINGDOM OF SAUDI ARABIA



Faculty of Science
Al Furat University
Dear El Zore, SYRIA

Faculty of Arts Science at Al Qurayat
Al-Jouf University, KINGDOM OF SAUDI ARABIA
Abstract. Let
be the
connected real semisimple Lie
group. Let
be the affine
group, which is the semidirect product of the two groups
with
, whivh plays an important role in technology. The
purpose of this paper is to define the Fourier transform in order to obtain
the Plancherel formula for the group
, and then we
establish the Plancherel theorem for the group
. To this end a Plancherel theorem for the affine group
will be obtained
Received: March 18, 2014
AMS Subject Classification: 43A30, 35D05
Key Words and Phrases: Iwasawa decomposition, affine group
, Fourier transform, Plancherel theorem
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DOI: 10.12732/ijpam.v93i5.9 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 5
Pages: 699 - 714
