2022/02/14 by Y. I. Akakpo, Akakpo, Y. I., Kofi V. S. Assiamoua +7
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Advanced Topics in Algebra #Compact group #Computer science #Extension (predicate logic) #FOS: Mathematics #Fourier transform #Functional Analysis (math.FA) #Geometry #Integral equation #Invertible matrix #Lie group #Locally compact group #Locally compact space #Mathematical analysis #Mathematics #Measure (data warehouse) #Noncommutative harmonic analysis #Orthogonality #Pure mathematics #Representation (politics) #Riemann–Stieltjes integral #Stability and Controllability of Differential Equations #Unitary representation #math.FA
paper · pdf · doi:10.48550/arxiv.2202.07055
published in arXiv (Cornell University) (Cornell University) · 15 pages
arxiv created 2022/02/14 · openalex publication_date 2022/02/14 · arxiv updated 2022/02/16 · openalex created_date 2022/04/03 · openalex updated_date 2026/08/06
In this work we extend the Fourier-Stieltjes transform of a vector measure and a continuous function defined on compact groups to locally compact groups. To do so, we consider a representation L of a normal compact subgroup K of a locally compact group G, and we use a representation of G induced by that of L. Then, we define the Fourier-Stieltjes transform of a vector measure and that of a continuous function with compact support defined on G from the representation of G. Then, we extend the Shur orthogonality relation established for compact groups to locally compact groups by using the representations of G induced by the unitary representations of one of its normal compact subgroups. This extension enables us to develop a Fourier-Stieltjes transform in series form that is linear, continuous, and invertible.