A note on Abel polynomials and rooted labeled forests
A special case of the Abel polynomials counts rooted labeled forests. This interpretation is used to obtain a combinatorial proof of the formula expressing x^n as a sum of these polynomials.
From sets to functions: Three elementary examples
A sequence of binomial type is a basis for R[x] satisfying a binomial-like identity, e.g. powers, rising and falling factorials. Given two sequences of binomial type, the authors describe a totally combinatorial way of finding the change of basis matrix: to each pair of sequences is associated a poset whose Whitney numbers of the 1st and 2nd kind give the entries of the matrix and its inverse.
ASYMPTOTIC PROPERTIES OF SOME CLASSES OF GENERALIZED FUNCTIONS
This paper studies the connection between the asymptotic and quasi-asymptotic properties at infinity of slowly increasing generalized functions with supports on the half-line and the asymptotic and quasi-asymptotic properties of the real parts of their Laplace and Fourier transforms in a neighborhood of the origin. The study is caried out in the scale of regularly varying self-similar functions. The results are applied to the study of the asymptotic properties of solutions of linear passive systems, and also to the study of the connection between Abel and Ces?ro convergence (with respect to a self-similar weight) of the Fourier-Stieltjes series of nonnegative measures. Bibliography: 13 titles.