6 papers
Fourier and Helgason Fourier transforms for Vector Bundle-valued Differential Forms on Homogeneous Spaces
Olufemi O. Oyadare
The major aim of studying harmonic analysis on any group or symmetric space is to understand enough of its structure to be able to prove the fundamental theorem on it via the Fouri…
What is the JEFT?
O. O. Oyadare
The JEFT is the acronym for the Joint-Eigenspace Fourier Transform defined on a noncompact symmetric space. It is a consequence of a general construction of a Fourier transform mod…
On the Lie algebra of a Malcev algebra
Olufemi O. Oyadare
This paper develops the structure theory of a Malcev algebra via the consideration of its most important and largest Lie (sub-) algebra. We introduce the notion of a Lie algebra wh…
A note on the harmonic analysis of the Joint-Eigenspace Fourier transform
O. O. Oyadare
We consider the irreducibility of the regular representation of a noncompact semisimpe Lie group on the Hilbert space of the image of the Joint-Eigenspace Fourier transform on…
Paley-Wiener theorem for the Joint-Eigenspace Fourier transform on noncompact symmetric spaces
Olufemi O. Oyadare
This paper conducts a geometric analysis of the Joint-Eigenspace Fourier transform of the symmetric space of the non-compact type. Our study shows how the Poisson transform builds…
On the operator-valued Fourier transform of the Harish-Chandra Schwartz Algebra
Olufemi O. Oyadare
We establish a type decomposition of the Harish-Chandra Schwartz algebra for any real-rank reductive group with a maximal compact subgroup and…