arXiv subjects

Bogdan M. Baishanski

Publications and source records attributed to Bogdan M. Baishanski.

2 recordsLinked to original sources

arXiv2008

A more intuitive definition of limit

Limit can be defined by two axioms: 1. Strict inequality between limits implies, ultimately, strict inequality between functions. 2. For constant functions limit is trivial. How can basic results on convergence be derived from these axioms? In this paper we propose two answers: a) at the most elementary level- add two more axioms, b) at somewhat higher level, do it in three steps, and, in our forthcoming paper "Axiomatic definition of limit", a third answer- c) do it neater - in an abstract framework, where only order relations are present.

math.HO↗

arXiv2008

An Asymptotic Formula for the Sequence ||exp(i n h(t))||_A

Given a function f with an absolutely convergent Fourier series, we define the norm of f as ||f||_A = the sum of absolute values of the Fourier coefficients of f. We study the behavior of ||f^n||_A as n goes to infinity, for f of the form exp(ih(t)) where h is a real, odd and twice continuously differentiable function such that h(t + 2π) = h(t) + 2kπfor some integer k. We obtain a remarkably simple asymptotic formula for the case when h'' has no zeros in (0,π) and satisfies an additional condition near 0 and near π. Corollaries of our formula are an asymptotic formula due to D.Girard, and a formula on Bessel functions, due to G.Stey.

math.CV↗