Gibbs derivatives on finite groups. Linear systems on finite non-Abelian groups. Hilbert transform on finite groups. Among the highlights is an in-depth coverage of applications of abstract harmonic analysis on
Gibbs derivatives on finite groups Linear systems on finite non-Abelian groups Hilbert transform on finite groups Among the highlights is an in-depth coverage of applications of abstract harmonic analysis on finite non-Abelian groups in compact representations of discrete functions and related tasks in...
Then using the Fourier analysis on finite abelian groups, they studied the nonlinearity of f by the Fourier transforms fx of fx , for all x ∈ X . To study the nonlinearity of functions on X , there is a different approach in [7,8]. By introducing a G-dual set X of the G-set ...
The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous ...
LetGbe a finite abelian group acting on a finite setX, and letfbe a complex valued function onX. For any, Poinsot et al. [13,15] defined a functiononGby, for all. Then using the Fourier analysis on finite abelian groups, they studied the nonlinearity offby the Fourier transformsof, f...
The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous ...
in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while...
It is also instrumental in analysis of boolean functions [6], [12] and more generally in theoretical computer science and learning theory [16]. From a computational point of view, an O(nlogn) algorithm is known for both the DFT and the WH transform. For the DFT case, this was ...
Journal of Functional Analysis, Volume 277, Issue 3, 1 August 2019, Pages 958-964 Hun Hee Lee, Ebrahim Samei, Nico SpronkView PDFAbstract We show that for a locally compact group G, amongst a class which contains amenable and small invariant neighbourhood groups, its Fourier algebra A(G) ...
The Fourier transform on compact groups is a major tool in representation theory (Knapp 2001) and non-commutative harmonic analysis. Let G be a compact Hausdorff topological group. Let Σ denote the collection of all isomorphism classes of finite-dimensional irreducible unitary representations, along ...