Absolute summation of Fourier integrals with multiplier by G.F. Voronoi method

Known and New Results on Absolute Convergence of Fourier Integrals

New sufficient conditions for representation of a function via the absolutely convergent Fourier integral are obtained in the paper. In the main result, Theorem 1.1, this is controlled by the behavior near infinity of both the function and its derivative. This result is extended to any dimension d ≥ 2.

Summation of Fourier Series

A general summability method of different orthogonal series is given with the help of an integrable function θ. As special cases the trigonometric Fourier, Walsh-, Walsh-Kaczmarz-, Vilenkinand Ciesielski-Fourier series and the Fourier transforms are considered. For each orthonormal system a different Hardy space is introduced and the atomic decomposition of these Hardy spaces are presented. A s...

Summation of Fourier

GF(2) Based Polynomials Multiplier Using An Efficient Systolic Multiplier

This paper presents an area-time-efficient systolic structure for multiplication over GF(2 m ) based on irreducible all-one polynomial (AOP). A novel cut-set retiming to reduce the duration of the critical-path to one XOR gate delay is used. Also the systolic structure can be decomposed into two or more parallel systolic branches, where the pair of parallel systolic branches has the same input ...

Numerical Calculation of Certain Definite Integrals by Poisson's Summation Formula

It is generally agreed that of all quadrature formulae, the trapezoidal rule, while being the simplest, is also the least accurate. There is, however, a rather general class of integrals for which the trapezoidal rule can be shown to be a highly accurate means of obtaining numerical values. Specifically, if the integrand is a periodic, even function with all derivatives continuous, then the int...