Applying results of the infinitary Ramsey theory, namely the dichotomy principle of Galvin-Prikry, we show that for every sequence of scalars, there exists a subsequence such that either every subsequence of defines a universal series, or no subsequence of defines a universal series. In particular examples we decide which of the two cases holds.
An infinite series which arises in certain applications of the Lagrange-Bürmann formula to exponential functions is investigated. Several very exact estimates for the Laplace transform and higher moments of this function are developed.
Let be a regular Jordan curve. In this work, the approximation properties of the -Faber-Laurent rational series expansions in the weighted Lebesgue spaces are studied. Under some restrictive conditions upon the weight functions the degree of this approximation by a th integral modulus of continuity in spaces is estimated.