arXiv subjects

Kahar El-Hussein

Publications and source records attributed to Kahar El-Hussein.

6 recordsLinked to original sources

arXiv2016

Plancherel Theorem on the Symplectic Group SP(4,R)

Let H be the 15- dimensional connected semisimple Lie group with its Iwasawa decomposition of H. Let G be the group of the semi direct product of H and the four dimensional real vector group . The goal of this paper is to define the Fourier transform in order to obtain the Plancherel theorem on H and so on G. Since its symplectic group of dimension 10 is a subgroup of H, then it will be easy to get the Plancherel theorem on the symplectic group and so on its inhomogeneous group. To this end, we obtain some interesting results on its nilpotent symplectic group

math.CA↗

arXiv2016

Abstract Harmonic Analysis On the non Singular Matrix Lie Group

As well known that it is no way to do the abstract harmonic analysis on the non connected Lie groups. The goal of this paper is to draw the attention of Mathematicians to solve this problem. therefore let R be the group of nonzero real numbers with multiplication and let H be the 3-dimensional Heisenberg group. I denote by G the semi direct of the Heisenberg group with R3 which is non connected solvable Lie group, and isomorphic onto the 6- dimensional non singular triangular matrix Lie group. I define the Fourier-Mellin transform and establish the Plancherel theorem on the group G. Besides I prove the solvability of any non zero invariant differential operator on the identity component of the group G. Finally, I give a classification of all left ideals of the its group algebra

math-ph↗

arXiv2016

Plancherel Theorem and the Left Ideals of the Group Algebra for the Jacobi Group

Let G be the three dimensional connected real semisimple Lie group and let KAN be the Iwasawa decomposition of G.Let J be the Jacobi group, which is the semidirect product of the two groups Heisenberg group with G. The Jacobi group plays an important role in Quantum Mechanics. The purpose of this paper is to define the Fourier transform in order to obtain the Plancherel theorem for the group J. To this end a classification of all left ideals of the group algebra for the Jacobi group

math.RT↗

arXiv2014

Abstract Harmonic Analysis on the General Affine Group GA(n,R)

The general linear group has two components and its the identity component, which consists of the real matrices with positive determinant and the set of all matrices with negative determinant. Since the general linear group is a two copies of the group of the identity component, so the general affine group. Consider the affine group, which is the semidirect product of the identity component with the real group of dimension. In this paper we generalize the Fourier transform to obtain the Plancherel theorem on this group and then, we establish the Plancherel theorem for the general affine group

math.RT↗

arXiv2014

Abstract Harmonic Analysis on the General Linear Group GL(n,R)

Consider the general linear group, which is not connected but rather has two connected components, the matrices with positive determinant and the ones with negative determinant. Consider the Iwasawa decomposition of its special linear group. We adopt the technique of the paper [12] to generalize the definition of the Fourier transform and to obtain the Plancherel theorem for the special linear group. Besides we prove that the component with negative determinant has a structure of group, which is isomorphic onto the group of the component with positive determinant in order to obtain the Plancherel theorem the general linear group

math.RT↗

arXiv2014

Abstract Harmonic Analysis on Spacetime

In this paper, we consider the Poincare group (space time). In mathematics, the Poincaré group of spacetime, named after Henri Poincaré, is the group of isometries of Minkowski spacetime, introduced by Hermann Minkowski. It is a non-abelian Lie group with ten generators. Spacetime, in physical science, single concept that recognizes the union of space and time, posited by Albert Einstein in the theories of relativity. One of the interesting problems for Mathematicians and Physicists is. Can we do the Fourier analysis on space time. The purpose of this paper is to define the Fourier transform the Poincaré group, and then we establish the Plancherel theorem for spacetime

math-ph↗