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...

Lanczos has recently developed a method for accelerating the convergence of trigonometric approximations for smooth, nonperiodic functions by modifying their boundary behavior. The method is reformulated here in terms of interpolation theory and is shown to be related to the theory of Lidstone interpolation. Extensions given include a new type of modifying function and the establishment of crit...

Some new inequalities for certain trigonometric polynomials with complex semiconvex and complex convex coefficients are given.

With the notation K := R (mod 2π),

In this paper, the k-trigonometric functions over the Galois Field GF(q) are introduced and their main properties derived. This leads to the definition of the cask(.) function over GF(q), which in turn leads to a finite field Hartley Transform . The main properties of this new discrete transform are presented and areas for possible applications are mentioned.

Let f be a piecewise analytic function on the unit interval (respectively, the unit circle of the complex plane). Starting from the Chebyshev (respectively, Fourier) coefficients of f , we construct a sequence of fast decreasing polynomials (respectively, trigonometric polynomials) which “detect” the points where f fails to be analytic, provided f is not infinitely differentiable at these points.

We show that finite-dimensional univariate function spaces satisfying a Bernstein-like inequality admit norming meshes. In particular, we determine meshes with “optimal” cardinality for trigonometric polynomials on subintervals of the period. As an application we discuss the construction of optimal bivariate polynomial meshes by arc blending. 2000 AMS subject classification: 26D05, 42A05, 65T40.

A numerical technique for solving a second-order nonlinear Neumann problem is presented. The authors approach is based on trigonometric scaling function on [0, 2π] which is constructed for Hermite interpolation. Two test problems are presented and errors plots show the efficiency of the proposed technique for the studied problem. 2000 Mathematics Subject Classification: 65L10, 65L60.

We prove bispectral duality for the generalized Calogero–Moser–Sutherland systems related to configurations An,2(m), Cn(l,m). The trigonometric axiomatics of Baker–Akhiezer function is modified, the dual difference operators of rational Macdonald type and the Baker–Akhiezer functions related to both series are explicitly constructed.

Using the new generalized exp-function method, we were able to derive significant novel closed form solutions nonlinear dispersive modified Benjamin–Bona–Mahony (DMBBM) equation. The general framework of method has been given. Many have obtained in hyperbolic, trigonometric, and rational function solutions. computer application Wolfram Mathematica 10, plotted 2D, 3D, contour surfaces found this...