Fourier transform and Plancherel Theorem for Nilpotent Lie Group

Kahar El-Hussein

doi:https://doi.org/10.14445/22315373/IJMTT-V4I11P5

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 4 | Issue 11 | Year 2013 | Article Id. IJMTT-V4I11P5 | DOI : https://doi.org/10.14445/22315373/IJMTT-V4I11P5

Fourier transform and Plancherel Theorem for Nilpotent Lie Group

Kahar El-Hussein

Abstract

As will known the connected and simply connected nilpotent Lie group N has an important role in quantum mechanics. In this paper we show how the Fourier transform on the n  dimensional vector Lie group n R can be generalized to N in order to obtain the Plancherel theorem. In addition we define the Fourier transform for the subgroup NA = A  N of the real semi-simple Lie group SL(n,R) to get also the Plancherel formula for NA

Keywords

Nilpotent Lie Group, Semi-simple Lie Group , Fourier Transform and Plancherel Theorem

References

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Citation :

Kahar El-Hussein, "Fourier transform and Plancherel Theorem for Nilpotent Lie Group," International Journal of Mathematics Trends and Technology (IJMTT), vol. 4, no. 11, pp. 288-294, 2013. Crossref, https://doi.org/10.14445/22315373/IJMTT-V4I11P5