Abstract Harmonic Analysis on Spacetime.
@article{ElHussein2014AbstractHA, title={Abstract Harmonic Analysis on Spacetime.}, author={Kahar El-Hussein}, journal={arXiv: Mathematical Physics}, year={2014} }
Let G = SL(2,C) be the 2×2 connected complex Lie group and let P = R 4 ⋊SL(2, C) be the Poincare group (space time). In mathemat- ics, the Poincare group (spacetime), named after Henri Poincare, is the group of isometries of Minkowski spacetime, introduced by Hermann Minkowski. It is a non-abelian Lie group with 10 generators. Space- time, in physical science, single concept that recognizes the union of space and time, posited by Albert Einstein in the theories of relativ- ity (1905, 1916). One…
One Citation
Abstract Harmonic Analysis on the General Affine Group GA(n,R)
- Mathematics
- 2014
Let GL(n,R) be the general linear group and let SL(n,R) = KAN be the Iwasawa decomposition of real connected semisimple Lie group SL(n,R). We adopt the technique in my paper [12] to generalize the…
References
SHOWING 1-10 OF 19 REFERENCES
The Fourier transform in quantum group theory (
- Mathematics
- 2007
The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this talk, I will discuss…
Abstract Harmonic Analysis and Ideals of Banach Algebra on 3-Step Nilpotent Lie Groups
- Mathematics
- 2013
Harmonic Analysis and Ideals of Banach Algebra on 3-Step Nilpotent Lie Groups. Kahar El-Hussein Department of Mathematics, Faculty of Science, Al-Fourat University, Deir-El-Zore, Syria Department of…
On the Left Ideals of Group Algebra of the Affine Group
- Mathematics
- 2011
From the fact that the affine group G = R� ρ Rhas only two equivalence classes of unitary irreducible representations, as such it is difficult to do its non commutative Fourier analysis. The aim of…
Non Commutative Fourier Transform on Some Lie Groups and Its Application to Harmonic Analysis
- Mathematics
- 2013
This paper will focus on Fourier transform on the semidirect product of two Lie groups to obtain some results in abstract harmonic analysis. In fact the combining of the classical Fourier transform…
Fourier Analysis on Groups
- Mathematics
- 1962
In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact…
Plancherel Formula for the 2 x 2 Real Unimodular Group.
- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1952
1 This result was previously obtained, by a method differing from ours, by Graeub, W., "Die Semilinearen Abbildungen," Sitzungsber. Heidelberger Akad. Wissensch., 1950, § 3, Satz 2. 2 Newman, M. H.…
Minkowski spacetime : a hundred years later
- Physics
- 2010
Preface Hermann Minkowski: Space and Time (English translation by Dennis Lehmkuhl) Hermann Minkowski: Raum und Zeit (original German text) PART I: The Impact of Minkowski Spacetime on the Twentieth…
Eigendistributions for the Invariant Differential Operators on the Affine Group
- Mathematics
- 2009
It is known that χξ(x )= e −i are eigendistributions for any invariant differential operator on R 2 . In this paper, we show that if T is an eigendistribution of an invariant differential operator on…
Opérateurs différentiels invariants sur les groupes de déplacements
- Physics
- 1988
Soit K un groupe de lie compact connexe, operant lineairement dans un espace vectoriel reel de dimension finie V, et soit G le groupe de deplacements, produit semi-direct de v par K. Pour la classe…