In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions  for a weighted Lebesgue space  $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$.  Among the other things, we also show that if $K$ is a locally compact hyper...

We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates. It appears that one can compute the limits of all noncommutative moments (thus all spectral properties) of the random matrices we consider because, when embedded in a space of larger square matrices, independent rectangular random matrices are asymptotically fre...

Discrete Convolution First of all we need to introduce what we might call the “wraparound” convention. Because the complex numbers wj = e i 2πj N have the property wj±N = wj, which readily extends to wj+mN = wj for any integer m, and since in the discrete Fourier context we represent all N -dimensional vectors as linear combinations of the Fourier vectors Wk whose components are wkj , we make t...

We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates. It appears that one can compute the limits of all non commutative moments (thus all spectral properties) of the random matrices we consider because, when embedded in a space of larger square matrices, independent rectangular random matrices are asymptotically fr...

The symmetric-convolution multiplication (SCM) property of discrete trigonometric transforms (DTTs) based on unitary transform matrices is developed. Then as the reciprocity of this property, the novel multiplication symmetric-convolution (MSC) property of discrete trigonometric transforms, is developed.

For the Maxwell’s equations in a Havriliak–Negami (H-N) dispersive medium, associated energy dissipation law has not been settled at both continuous level and discrete level. In this paper, we rigorously show that of H-N model can be bounded by initial is well-posed. We analyse backward Euler-type semi-discrete scheme, prove modified decays monotonically time. Such strong stability ensures sche...

 Abstract—Discrete trigonometric transformations, such as the discrete Fourier and cosine/sine transforms, are important in a variety of applications due to their useful properties. For example, one well-known property is the convolution theorem for Fourier transform. In this letter, we derive a discrete Fresnel transform (DFnT) from the infinitely periodic optical gratings, as a linear trigon...