3 citations · 4 across the 16 of their papers we have counts for
17 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…
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…
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…
Functional analysis of canonical wave-packets on real reductive groups
Olufemi O. Oyadare
This paper revisits the study of canonical wave-packets on a real reductive groups, sequel to its construction in a recent manuscript of Oyadare. Among other results, we prove some…
The full Bochner theorem on real reductive groups
Olufemi O. Oyadare
The major results of Barker leading to the spherical Bochner theorem and its (spherical) extension, were made possible through the spherical transform theory of Trombi-Vara…
Non-spherical Harish-Chandra Fourier transforms on real reductive groups
Olufemi O. Oyadare
The Harish-Chandra Fourier transform, is a linear topological algebra isomorphism of the spherical (Schwartz) convolution algebra (w…
Abstract Peter-Weyl theory for semicomplete orthonormal sets
Olufemi O. Oyadare
The central concept in the harmonic analysis of a compact group is the completeness of Peter-Weyl orthonormal basis as constructed from the matrix coefficients of a maximal set of…
Non-gaussian congruences
Olufemi O. Oyadare
This paper is an invitation to the study and use of general theory of non-gaussian congruences in the theory of numbers. In this work we classify the two kinds of congruenc…
On harmonic analysis of spherical convolutions on semisimple Lie groups
Olufemi O. Oyadare
This paper contains a non-trivial generalization of the Harish-Chandra transforms on a connected semisimple Lie group with finite center, into what we term spherical convoluti…
Differential equations and the algebra of confluent spherical functions on semisimple Lie groups
Olufemi O. Oyadare
We consider the notion of a confluent spherical function on a connected semisimple Lie group, with finite center and of real rank and discuss the properties and relations…
Series Analysis and Schwartz Algebras of Spherical Convolutions on Semisimple Lie Groups
Olufemi O. Oyadare
We give the exact contributions of Harish-Chandra transform, of Schwartz functions to the harmonic analysis of spherical convolutions and the corresponding…
On Quasi-Symmetric Polynomially Bounded Fréchet Algebras
Olufemi O. Oyadare
This paper concerns the notion of a symmetric algebra and its generalization to a quasi-symmetric algebra. We study the structure of these algebras in respect to their hull-kernel…
Fourier Transform of Schwartz Algebras on Groups in the Harish-Chandra class
Olufemi O. Oyadare
It is well-known that the Harish-Chandra transform, is a topological isomorphism of the spherical (Schwartz) convolution algebra (wh…
Galois groups of Fermat polynomials and the arithmetic groups of Diophantine curves
Olufemi O. Oyadare
This paper develops a framework of algebra whereby every Diophantine equation is made quickly accessible by a study of the corresponding row entries in an array of numbers which we…