An Asymptotic Formula for the Sequence ||exp(i n h(t))||_A
| dc.creator | Baishanski, Bogdan M. | |
| dc.creator | Hlavacek, Jan | |
| dc.date | 2008-05-12 | |
| dc.date | 2008-05-13 | |
| dc.date.accessioned | 2026-07-07T09:38:25Z | |
| dc.date.available | 2026-07-07T09:38:25Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0805.1699 | |
| dc.identifier | http://arxiv.org/abs/0805.1699 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160799 | |
| dc.subject | Complex Variables | |
| dc.subject | 41A60, 42A16 | |
| dc.title | An Asymptotic Formula for the Sequence ||exp(i n h(t))||_A | |
| dc.type | text |