Let GH(n; G) denote a generalised Hadamard matrix of order n over the group G, and let EA( q) denote the elementary abelian group of prime power order q. We use a computer to investigate the applicability of a recently discovered general construction for GH (4tq; E A( q)) in the case t = 2. In particular, we prove that G H (8p; Zp) exist for all primes p > 19, and obtain GH(8q; EA(q)) for all p...

This paper is concerned with the definitions of the discrete fractional Hartley transform (DFRHT) and the discrete fractional Fourier transform (DFRFT). First, the eigenvalues and eigenvectors of the discrete Fourier and Hartley transform matrices are investigated. Then, the results of the eigendecompositions of the transform matrices are used to define DFRHT and DFRFT. Also, an important relat...

If at each point of a set of positive Lebesgue measure, every rearrangement of a multiple trigonometric series square converges to a finite value, then that series is the Fourier series of a function to which it converges uniformly. If there is at least one point at which every rearrangement of a multiple Walsh series square converges to a finite value, then that series is the Walsh-Fourier ser...