We continue our study of intermediate sums over polyhedra, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasipolynomial of a rational simplex, Math. Comp. 75 (2006), 1449– 1466]. By well-known decompositions, it is sufficient to consider the case of affine cones s+c, where s is an arbitrary real vertex and c is a rational polyhed...

This paper is devoted to the acceleration of convergence partial sums classical Fourier series for sufficiently smooth functions. Some universal and adaptive algorithms are constructed studied. It shown that use a finite number coefficients makes it possible exact approximation given function from an infinite-dimensional set quasi-polynomials. In this sense, we call corresponding essentially no...

These were not the first estimates for E,* but they were the cleanest. Only a year earlier, Lebesguc had given estimates for approximation by the nth Fourier sums; but the latter contain logarithms which are absent in (3). As natural as (3) seems, there is still the question whether it is in some sense best possible. Bernstein [2] showed that this is the case, in at least two different ways. He...

It is shown in a previous work that Faber-Pandharipande-Zagier's and Miki's identities can be derived from a polynomial identity, which in turn follows from the Fourier series expansion of sums of products of Bernoulli functions. Motivated by and generalizing this, we consider three types of functions given by sums of products of higher-order Bernoulli functions and derive their Fourier series ...